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Message #03671
Re: [Bug 511929] Re: Missing domain_type
On Tue, Feb 02, 2010 at 11:56:10AM +0100, Mehdi Nikbakht wrote:
> On Tue, 2010-02-02 at 11:52 +0100, Anders Logg wrote:
> > On Tue, Feb 02, 2010 at 11:24:46AM +0100, Mehdi Nikbakht wrote:
> > > On Tue, 2010-02-02 at 11:18 +0100, Anders Logg wrote:
> > > > On Tue, Feb 02, 2010 at 11:16:20AM +0100, Mehdi Nikbakht wrote:
> > > > > On Tue, 2010-02-02 at 10:50 +0100, Anders Logg wrote:
> > > > > > On Tue, Feb 02, 2010 at 10:42:23AM +0100, Mehdi Nikbakht wrote:
> > > > > > >
> > > > > > >
> > > > > > > On Tue, 2010-02-02 at 10:30 +0100, Anders Logg wrote:
> > > > > > > > I tried looking at this but I'm unsure how it should be
> > > > > > > > handled. Should a cell_integral class be generated or should a
> > > > > > > > surface_integral class be generated?
> > > > > > > >
> > > > > > >
> > > > > > > We handle terms related to surface integral inside a class derived from
> > > > > > > ufc::cell_integral. I have started working on updating ffcpum module
> > > > > > > which is built against standard ffc.
> > > > > > >
> > > > > > > Mehdi
> > > > > >
> > > > > > So a surface integral should just result in a standard cell integral
> > > > > > being generated? Then what is the point of having *dc? When the code
> > > > > > has been generated, you won't be able to tell which cell integrals
> > > > > > came from *dx and which came from *dc.
> > > > >
> > > > > Although we could have them in a separate class, we handle them inside
> > > > > cell_integral class to have compatibility with ufc interface.
> > > > >
> > > > > Note that having *dc helps us to compute the corresponding terms by
> > > > > using gauss points located on a surface.
> > > > >
> > > > > I don't see the point on being able to tell which cell integrals came
> > > > > from *dx and which one from *dc, we add all of them to the global
> > > > > element tensor.
> > > >
> > > > My point is that if FFC should treat *dc in exactly the same way as
> > > > *dx, then you might as well just write *dx and we can remove the
> > > > "support" for *dc in FFC.
> > > >
> > > > Or you could just write dc = dx in your form files.
> > >
> > > No, it is not the case. They are handled differently inside ffc, we only
> > > add them inside ufc::cell_integral in the code generation stage.
> >
> > ok, so the code example you sent me (Poisson.h) is code generated by
> > FFC? Not a version you have modified. I didn't know that was
> > supported.
>
> No, this is generated by ffc-pum which is a module on the top of
> standard ffc. To compile this file, one need just run,
>
> >> ffcpum -l dolfin Poisson.ufl
Then I don't really understand what goes on. Should or should not FFC
treat surface integrals in exactly the same way as standard integrals?
--
Anders
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[num_derivatives + row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[6][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}, {{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[6][1] = {{1}, {1}, {1}, {1}, {1}, {1}};
> > > > > static const double D[6][1][2] = {{{1, 0}}, {{1, 0}}, {{1, 0}}, {{0, 1}}, {{0, 1}}, {{0, 1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[2];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 2; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[2] = dof_values[1];
> > > > > vertex_values[4] = dof_values[2];
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[1] = dof_values[3];
> > > > > vertex_values[3] = dof_values[4];
> > > > > vertex_values[5] = dof_values[5];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_0_finite_element_0_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_0_finite_element_0_1();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_0_finite_element_1_0: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_finite_element_1_0() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_0_finite_element_1_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_finite_element_1_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_0_finite_element_1_1: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_finite_element_1_1() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_0_finite_element_1_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_finite_element_1_1();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_0_finite_element_1: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_finite_element_1() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_0_finite_element_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 6;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > values[0] = 0;
> > > > > values[1] = 0;
> > > > >
> > > > > if (0 <= i && i <= 2)
> > > > > {
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > values[0] = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > if (3 <= i && i <= 5)
> > > > > {
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i - 3;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > values[1] = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 2*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > if (0 <= i && i <= 2)
> > > > > {
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > if (3 <= i && i <= 5)
> > > > > {
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i - 3;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[num_derivatives + row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[6][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}, {{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[6][1] = {{1}, {1}, {1}, {1}, {1}, {1}};
> > > > > static const double D[6][1][2] = {{{1, 0}}, {{1, 0}}, {{1, 0}}, {{0, 1}}, {{0, 1}}, {{0, 1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[2];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 2; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[2] = dof_values[1];
> > > > > vertex_values[4] = dof_values[2];
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[1] = dof_values[3];
> > > > > vertex_values[3] = dof_values[4];
> > > > > vertex_values[5] = dof_values[5];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_0_finite_element_1_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_0_finite_element_1_1();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_0_finite_element_2: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_finite_element_2() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_0_finite_element_2()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[1][1] = \
> > > > > {{1.41421356237309}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[1][1] = \
> > > > > {{1.41421356237309}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[1][1] = \
> > > > > {{0}};
> > > > >
> > > > > static const double dmats1[1][1] = \
> > > > > {{0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[1][1][2] = {{{0.333333333333333, 0.333333333333333}}};
> > > > > static const double W[1][1] = {{1}};
> > > > > static const double D[1][1][1] = {{{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[0];
> > > > > vertex_values[2] = dof_values[0];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_finite_element_2();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_0_finite_element_3: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_finite_element_3() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_0_finite_element_3()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_finite_element_3();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_0_dof_map_0_0: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_dof_map_0_0() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_0_dof_map_0_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_dof_map_0_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_0_dof_map_0_1: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_dof_map_0_1(const std::vector<const pum::GenericPUM*>& pums) :ufc::dof_map(), pums(pums)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_0_dof_map_0_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension + pums[0]->enriched_global_dimension();
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return pums[0]->enriched_local_dimension(c);
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return pums[0]->enriched_max_local_dimension();
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Generate code for tabulating extra degrees of freedom.
> > > > > unsigned int local_offset = 0;
> > > > > unsigned int global_offset = 0;
> > > > >
> > > > > // Calculate local-to-global mapping for the enriched dofs related to the discontinuous field 0
> > > > > pums[0]->tabulate_enriched_dofs(dofs, c, local_offset, global_offset);
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > const std::vector<const pum::GenericPUM*>& p0 = boost::assign::list_of(pums[0]);
> > > > >
> > > > > return new poisson_0_dof_map_0_1(p0);
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_0_dof_map_0: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_dof_map_0(const std::vector<const pum::GenericPUM*>& pums) :ufc::dof_map(), pums(pums)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_0_dof_map_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension + pums[0]->enriched_global_dimension();
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3 + pums[0]->enriched_local_dimension(c);
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3 + pums[0]->enriched_max_local_dimension();
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 4;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];\
> > > > >
> > > > > // Generate code for tabulating extra degrees of freedom.
> > > > > unsigned int local_offset = 3;
> > > > > unsigned int global_offset = m.num_entities[0];
> > > > >
> > > > > // Calculate local-to-global mapping for the enriched dofs related to the discontinuous field 0
> > > > > pums[0]->tabulate_enriched_dofs(dofs, c, local_offset, global_offset);
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > dofs[2] = 4;
> > > > > dofs[3] = 5;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > dofs[2] = 3;
> > > > > dofs[3] = 5;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > dofs[2] = 3;
> > > > > dofs[3] = 4;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > coordinates[3][0] = x[0][0];
> > > > > coordinates[3][1] = x[0][1];
> > > > > coordinates[4][0] = x[1][0];
> > > > > coordinates[4][1] = x[1][1];
> > > > > coordinates[5][0] = x[2][0];
> > > > > coordinates[5][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > const std::vector<const pum::GenericPUM*>& p1 = boost::assign::list_of(pums[0]);
> > > > >
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_0_dof_map_0_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_0_dof_map_0_1(p1);
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_0_dof_map_1_0: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_dof_map_1_0() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_0_dof_map_1_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_dof_map_1_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_0_dof_map_1_1: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_dof_map_1_1(const std::vector<const pum::GenericPUM*>& pums) :ufc::dof_map(), pums(pums)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_0_dof_map_1_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension + pums[0]->enriched_global_dimension();
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return pums[0]->enriched_local_dimension(c);
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return pums[0]->enriched_max_local_dimension();
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Generate code for tabulating extra degrees of freedom.
> > > > > unsigned int local_offset = 0;
> > > > > unsigned int global_offset = 0;
> > > > >
> > > > > // Calculate local-to-global mapping for the enriched dofs related to the discontinuous field 0
> > > > > pums[0]->tabulate_enriched_dofs(dofs, c, local_offset, global_offset);
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > const std::vector<const pum::GenericPUM*>& p0 = boost::assign::list_of(pums[0]);
> > > > >
> > > > > return new poisson_0_dof_map_1_1(p0);
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_0_dof_map_1: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_dof_map_1(const std::vector<const pum::GenericPUM*>& pums) :ufc::dof_map(), pums(pums)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_0_dof_map_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension + pums[0]->enriched_global_dimension();
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3 + pums[0]->enriched_local_dimension(c);
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3 + pums[0]->enriched_max_local_dimension();
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 4;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];\
> > > > >
> > > > > // Generate code for tabulating extra degrees of freedom.
> > > > > unsigned int local_offset = 3;
> > > > > unsigned int global_offset = m.num_entities[0];
> > > > >
> > > > > // Calculate local-to-global mapping for the enriched dofs related to the discontinuous field 0
> > > > > pums[0]->tabulate_enriched_dofs(dofs, c, local_offset, global_offset);
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > dofs[2] = 4;
> > > > > dofs[3] = 5;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > dofs[2] = 3;
> > > > > dofs[3] = 5;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > dofs[2] = 3;
> > > > > dofs[3] = 4;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > coordinates[3][0] = x[0][0];
> > > > > coordinates[3][1] = x[0][1];
> > > > > coordinates[4][0] = x[1][0];
> > > > > coordinates[4][1] = x[1][1];
> > > > > coordinates[5][0] = x[2][0];
> > > > > coordinates[5][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > const std::vector<const pum::GenericPUM*>& p1 = boost::assign::list_of(pums[0]);
> > > > >
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_0_dof_map_1_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_0_dof_map_1_1(p1);
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_0_dof_map_2: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_dof_map_2() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_0_dof_map_2()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return false;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return true;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[2];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[2][0];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > >
> > > > > break;
> > > > > case 1:
> > > > >
> > > > > break;
> > > > > case 2:
> > > > >
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
> > > > > coordinates[0][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_dof_map_2();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_0_dof_map_3: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_dof_map_3() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_0_dof_map_3()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_dof_map_3();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the tabulation of the cell
> > > > > /// tensor corresponding to the local contribution to a form from
> > > > > /// the integral over a cell.
> > > > >
> > > > > class poisson_0_cell_integral_0_quadrature: public ufc::cell_integral
> > > > > {
> > > > >
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > > mutable std::vector <double> Aa;
> > > > > mutable std::vector <double> Af;
> > > > >
> > > > >
> > > > >
> > > > > /// Tabulate the regular entities of tensor for the contribution from a local cell
> > > > > virtual void tabulate_regular_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * x = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = x[1][0] - x[0][0];
> > > > > const double J_01 = x[2][0] - x[0][0];
> > > > > const double J_10 = x[1][1] - x[0][1];
> > > > > const double J_11 = x[2][1] - x[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv_00 = J_11 / detJ;
> > > > > const double Jinv_01 = -J_01 / detJ;
> > > > > const double Jinv_10 = -J_10 / detJ;
> > > > > const double Jinv_11 = J_00 / detJ;
> > > > >
> > > > > // Set scale factor
> > > > > const double det = std::abs(detJ);
> > > > >
> > > > >
> > > > > // Array of quadrature weights
> > > > > static const double W1 = 0.5;
> > > > > // Quadrature points on the UFC reference element: (0.333333333333333, 0.333333333333333)
> > > > >
> > > > > // Value of basis functions at quadrature points.
> > > > > static const double FE0[1][3] = \
> > > > > {{0.333333333333333, 0.333333333333333, 0.333333333333333}};
> > > > >
> > > > > static const double FE1_C0_D01[1][6] = \
> > > > > {{-1, 0, 1, 0, 0, 0}};
> > > > >
> > > > > static const double FE1_C0_D10[1][6] = \
> > > > > {{-1, 1, 0, 0, 0, 0}};
> > > > >
> > > > > static const double FE1_C1_D01[1][6] = \
> > > > > {{0, 0, 0, -1, 0, 1}};
> > > > >
> > > > > static const double FE1_C1_D10[1][6] = \
> > > > > {{0, 0, 0, -1, 1, 0}};
> > > > >
> > > > >
> > > > > // local dimension of the current cell
> > > > > unsigned int offset = 3 + pums[0]->enriched_local_dimension(c);
> > > > >
> > > > >
> > > > > // Remove regular local dimension to obtain number of enriched dofs
> > > > > offset -= 3;
> > > > >
> > > > > // Compute element tensor using UFL quadrature representation
> > > > > // Optimisations: ('simplify expressions', False), ('ignore zero tables', False), ('non zero columns', False), ('remove zero terms', False), ('ignore ones', False)
> > > > > // Total number of operations to compute element tensor: 1266
> > > > >
> > > > > // Loop quadrature points for integral
> > > > > // Number of operations to compute element tensor for following IP loop = 1266
> > > > > // Only 1 integration point, omitting IP loop.
> > > > >
> > > > > // Function declarations
> > > > > double F0 = 0;
> > > > >
> > > > > // Total number of operations to compute function values = 6
> > > > > for (unsigned int r = 0; r < 3; r++)
> > > > > {
> > > > > F0 += FE0[0][r]*w[1][r];
> > > > > }// end loop over 'r'
> > > > > unsigned int m = 0;
> > > > >
> > > > > // Number of operations for primary indices = 1260
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > for (unsigned int k = 0; k < 6; k++)
> > > > > {
> > > > > if ((((0 <= j && j < 3)) && ((0 <= k && k < 3))))
> > > > > {
> > > > > // Number of operations to compute entry = 35
> > > > > A[m] += (((Jinv_00*FE1_C1_D10[0][j] + Jinv_10*FE1_C1_D01[0][j]) + (Jinv_00*FE1_C0_D10[0][j] + Jinv_10*FE1_C0_D01[0][j]))*((Jinv_00*FE1_C1_D10[0][k] + Jinv_10*FE1_C1_D01[0][k]) + (Jinv_00*FE1_C0_D10[0][k] + Jinv_10*FE1_C0_D01[0][k])) + ((Jinv_01*FE1_C0_D10[0][j] + Jinv_11*FE1_C0_D01[0][j]) + (Jinv_01*FE1_C1_D10[0][j] + Jinv_11*FE1_C1_D01[0][j]))*((Jinv_01*FE1_C1_D10[0][k] + Jinv_11*FE1_C1_D01[0][k]) + (Jinv_01*FE1_C0_D10[0][k] + Jinv_11*FE1_C0_D01[0][k])))*F0*W1*det;
> > > > >
> > > > > ++m;
> > > > > }
> > > > > }// end loop over 'k'
> > > > >
> > > > > // Offset the entries corresponding to enriched terms
> > > > > if ((((0 <= j && j < 3))))
> > > > > m += offset;
> > > > > }// end loop over 'j'
> > > > > }
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_cell_integral_0_quadrature(const std::vector<const pum::GenericPUM*>& pums) : ufc::cell_integral(), pums(pums)
> > > > > {
> > > > > //Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_0_cell_integral_0_quadrature()
> > > > > {
> > > > > //Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > /// Tabulate the tensor for the contribution from a local cell
> > > > > virtual void tabulate_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Tabulate regular entires of element tensor
> > > > > tabulate_regular_tensor(A, w, c);
> > > > >
> > > > > // local dimension of the current cell
> > > > > unsigned int num_entries = 3 + pums[0]->enriched_local_dimension(c);
> > > > >
> > > > >
> > > > > // Remove regular local dimension to obtain number of enriched dofs
> > > > > num_entries -= 3;
> > > > >
> > > > > if (num_entries == 0)
> > > > > return;
> > > > >
> > > > >
> > > > > // Extract vertex coordinates
> > > > > const double * const * x = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = x[1][0] - x[0][0];
> > > > > const double J_01 = x[2][0] - x[0][0];
> > > > > const double J_10 = x[1][1] - x[0][1];
> > > > > const double J_11 = x[2][1] - x[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > >
> > > > > // Set scale factor
> > > > > const double det = std::abs(detJ);
> > > > >
> > > > > // FIXME: It will crash for multiple discontinuities, if we don't have at least one cell which all dofs are enriched
> > > > > const unsigned int min_entries = 36;
> > > > > const unsigned int _num_entries = std::max(num_entries*num_entries, min_entries);
> > > > >
> > > > > // Resizing and reseting auxiliary tensors
> > > > > Aa.resize(_num_entries);
> > > > > std::fill(Aa.begin(), Aa.end(), 0.0);
> > > > >
> > > > > // Define an array to save current quadrature point
> > > > > double coordinate[2];
> > > > >
> > > > > // Define ufc::finite_element object(s) to evalaute shape functions or their derivatives on runtime
> > > > > poisson_0_finite_element_3 element_0;
> > > > > poisson_0_finite_element_0 element_1;
> > > > >
> > > > > // Array of quadrature weights
> > > > > static const double W1[1] = {0.5};
> > > > >
> > > > >
> > > > > // Array of quadrature points
> > > > > static const double P1[2] = \
> > > > > {0.333333333333333, 0.333333333333333};
> > > > >
> > > > > // Define vectors for quadrature points and weights(note that the sizes are determined in compile time)
> > > > > std::vector <double> Wn1;
> > > > > std::vector <double> Pn1;
> > > > >
> > > > >
> > > > > // Check whether there is any need to use modified integration scheme
> > > > > if ((pums[0]->modified_quadrature(c)))
> > > > > {
> > > > >
> > > > > const std::vector<double> weight1(W1, W1 + 1);
> > > > > const std::vector<double> point1(P1, P1 + 2);
> > > > >
> > > > > ConstQuadratureRule standard_gauss = std::make_pair(point1, weight1);
> > > > > QuadratureRule modified_gauss;
> > > > >
> > > > > pums[0]->cell_quadrature_rule(modified_gauss, standard_gauss, c);
> > > > >
> > > > > Pn1 = modified_gauss.first;
> > > > > Wn1 = modified_gauss.second;
> > > > >
> > > > > }
> > > > > else
> > > > > {
> > > > > // Map quadrature points from the reference cell to the physical cell
> > > > > Wn1.resize(1);;
> > > > > Pn1.resize(2);;
> > > > >
> > > > >
> > > > > for (unsigned int i = 0; i < 1; i++)
> > > > > {
> > > > > Wn1[i] = W1[i];
> > > > > for (unsigned int j = 0; j < 2; j++)
> > > > > Pn1[2*i + j] = x[0][j]*(1.0 - P1[2*i] - P1[2*i + 1]) + x[1][j]*P1[2*i + 1] + x[2][j]*P1[2*i];
> > > > > }
> > > > > }
> > > > >
> > > > >
> > > > > // Return the values of enriched function at the quadrature points
> > > > > std::vector<double> enriched_values_1;
> > > > > pums[0]->tabulate_enriched_basis(enriched_values_1, Pn1, c);
> > > > >
> > > > > // Define auxilary indices: m, n
> > > > > unsigned int m = 0;
> > > > > unsigned int n = 0;
> > > > >
> > > > >
> > > > > // Loop over new quadrature points for integral
> > > > > for (unsigned int ip = 0; ip < Wn1.size(); ip++)
> > > > > {
> > > > > // Evalaute tables and entries in the element tensor, if the enhanced value at this quadrature point is non-zero
> > > > > if (enriched_values_1[ip] != 0)
> > > > > {
> > > > > // Pick up the coordinates of the current quadrature point
> > > > > coordinate[0] = Pn1[2*ip];
> > > > > coordinate[1] = Pn1[2*ip + 1];
> > > > >
> > > > >
> > > > > // Creating a table to save the values of shape functions at the current guass point for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)
> > > > > double value_0[1];
> > > > > double table_0_D0[3][1];
> > > > > for (unsigned int j = 0; j < 3; j++)
> > > > > {
> > > > > element_0.evaluate_basis(j, value_0, coordinate, c);
> > > > > for (unsigned int k = 0; k < 1; k++)
> > > > > table_0_D0[j][k] = value_0[k];
> > > > > }
> > > > >
> > > > >
> > > > > // Creating a table to save the values of shape functions at the current guass point for MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })
> > > > > double value_1[2];
> > > > > double table_1_D0[6][2];
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > element_1.evaluate_basis(j, value_1, coordinate, c);
> > > > > for (unsigned int k = 0; k < 2; k++)
> > > > > table_1_D0[j][k] = value_1[k];
> > > > > }
> > > > >
> > > > >
> > > > > // Creating a table to save the values of derivatives order 1 at the current guass point for MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })
> > > > > double value_2[4];
> > > > > double table_1_D1[6][4];
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > element_1.evaluate_basis_derivatives(j, 1, value_2, coordinate, c);
> > > > > for (unsigned int k = 0; k < 4; k++)
> > > > > table_1_D1[j][k] = value_2[k];
> > > > > }
> > > > >
> > > > > // Function declarations
> > > > > double F0 = 0;
> > > > >
> > > > > // Total number of operations to compute function values = 6
> > > > > for (unsigned int r = 0; r < 3; r++)
> > > > > {
> > > > > F0 += table_0_D0[r][0]*w[1][r];
> > > > > }// end loop over 'r'
> > > > >
> > > > > // Number of operations for primary indices = 396
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > for (unsigned int k = 0; k < 6; k++)
> > > > > {
> > > > > if (!(((0 <= j && j < 3)) && ((0 <= k && k < 3))))
> > > > > {
> > > > > // Move the indices of discontinuous spaces to the end of mixed space
> > > > > if ((0 <= j && j < 3) && (3 <= k && k < 6))
> > > > > {
> > > > > m = j;
> > > > > n = k;
> > > > > }
> > > > > else if ((3 <= j && j < 6) && (0 <= k && k < 3))
> > > > > {
> > > > > m = j;
> > > > > n = k;
> > > > > }
> > > > > else if ((3 <= j && j < 6) && (3 <= k && k < 6))
> > > > > {
> > > > > m = j;
> > > > > n = k;
> > > > > }
> > > > > // Number of operations to compute entry = 11
> > > > > Aa[m*6 + n] += ((table_1_D1[j][0] + table_1_D1[j][2])*(table_1_D1[k][2] + table_1_D1[k][0]) + (table_1_D1[j][3] + table_1_D1[j][1])*(table_1_D1[k][3] + table_1_D1[k][1]))*F0*Wn1[ip]*det;
> > > > > }// end check for enriched entiries
> > > > > }// end loop over 'k'
> > > > > }// end loop over 'j'
> > > > > }
> > > > > }// end loop over 'ip'
> > > > >
> > > > > // Check whether the current cell is intersected by discontinuity
> > > > > if ((pums[0]->modified_quadrature(c)))
> > > > > {
> > > > > // Define ufc::finite_element object(s) to evalaute shape functions or their derivatives on runtime
> > > > > poisson_0_finite_element_2 element_0;
> > > > > poisson_0_finite_element_0 element_1;
> > > > >
> > > > > // Array of quadrature weights
> > > > > static const double W4[2] = {0.5, 0.5};
> > > > >
> > > > >
> > > > > // Array of quadrature points
> > > > > static const double P4[2] = \
> > > > > {0.211324865405187,
> > > > > 0.788675134594813};
> > > > >
> > > > > // Define vectors for quadrature points and weights
> > > > > std::vector <double> Wn4(2);
> > > > > std::vector <double> Pn4(4);
> > > > >
> > > > >
> > > > > const std::vector<double> weight4(W4, W4 + 2);
> > > > > const std::vector<double> point4(P4, P4 + 2);
> > > > >
> > > > > ConstQuadratureRule standard_gauss = std::make_pair(point4, weight4);
> > > > > QuadratureRule modified_gauss;
> > > > >
> > > > > pums[0]->surface_quadrature(modified_gauss, standard_gauss, c);
> > > > >
> > > > > Pn4 = modified_gauss.first;
> > > > > Wn4 = modified_gauss.second;
> > > > >
> > > > >
> > > > > // Define and initialize the determinant of Jacobian
> > > > > const double det = 1.0;
> > > > >
> > > > > // Loop over new quadrature points for integral
> > > > > for (unsigned int ip = 0; ip < Wn4.size(); ip++)
> > > > > {
> > > > > // Pick up the coordinates of the current quadrature point
> > > > > coordinate[0] = Pn4[2*ip];
> > > > > coordinate[1] = Pn4[2*ip + 1];
> > > > >
> > > > >
> > > > > // Creating a table to save the values of shape functions at the current guass point for MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })
> > > > > double value_0[2];
> > > > > double table_1_D0[6][2];
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > element_1.evaluate_basis(j, value_0, coordinate, c);
> > > > > for (unsigned int k = 0; k < 2; k++)
> > > > > table_1_D0[j][k] = value_0[k];
> > > > > }
> > > > >
> > > > >
> > > > > // Creating a table to save the values of shape functions at the current guass point for FiniteElement('Discontinuous Lagrange', Cell('triangle', 1, Space(2)), 0)
> > > > > double value_1[1];
> > > > > double table_0_D0[1][1];
> > > > > for (unsigned int j = 0; j < 1; j++)
> > > > > {
> > > > > element_0.evaluate_basis(j, value_1, coordinate, c);
> > > > > for (unsigned int k = 0; k < 1; k++)
> > > > > table_0_D0[j][k] = value_1[k];
> > > > > }
> > > > >
> > > > > // Number of operations for primary indices = 180
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > for (unsigned int k = 0; k < 6; k++)
> > > > > {
> > > > > if (!(((0 <= j && j < 3)) || ((0 <= k && k < 3))))
> > > > > {
> > > > > // Move the indices of discontinuous spaces to the end of mixed space
> > > > > if ((3 <= j && j < 6) && (3 <= k && k < 6))
> > > > > {
> > > > > m = j;
> > > > > n = k;
> > > > > }
> > > > > // Number of operations to compute entry = 5
> > > > > Aa[m*6 + n] += table_1_D0[j][1]*table_1_D0[k][1]*w[0][0]*Wn4[ip]*det;
> > > > > }// end check for enriched entiries
> > > > > }// end loop over 'k'
> > > > > }// end loop over 'j'
> > > > > }// end loop over 'ip'
> > > > > }
> > > > >
> > > > >
> > > > > // Pick up entries from the total element tensor for the nodes active in the enrichment
> > > > >
> > > > > // Determine a vector that contains the local numbering of enriched degrees of freedom in ufc::cell c for the field 0
> > > > > std::vector<unsigned int> active_dofs_0;
> > > > > pums[0]->tabulate_enriched_local_dofs(active_dofs_0, c);
> > > > > std::vector<unsigned int>::iterator it_0_0, it_0_1;
> > > > >
> > > > >
> > > > > m = 0;
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > for (unsigned int k = 0; k < 6; k++)
> > > > > if ((0 <= j && j < 3) && (0 <= k && k < 3))
> > > > > ++m;
> > > > > else
> > > > > {
> > > > > it_0_0 = find(active_dofs_0.begin(), active_dofs_0.end(), j - 3);
> > > > > it_0_1 = find(active_dofs_0.begin(), active_dofs_0.end(), k - 3);
> > > > >
> > > > >
> > > > > // Check whether the entry is coressponding to the active enriched node
> > > > > if (it_0_0 != active_dofs_0.end() || it_0_1 != active_dofs_0.end())
> > > > > if (((0 <= j && j < 3)) || ((0 <= k && k < 3)) || (it_0_0 != active_dofs_0.end() && it_0_1 != active_dofs_0.end()))
> > > > > {
> > > > > A[m] = Aa[j*6 + k];
> > > > > ++m;
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the tabulation of the cell
> > > > > /// tensor corresponding to the local contribution to a form from
> > > > > /// the integral over a cell.
> > > > >
> > > > > class poisson_0_cell_integral_0: public ufc::cell_integral
> > > > > {
> > > > > private:
> > > > >
> > > > > poisson_0_cell_integral_0_quadrature* integral_0_quadrature;
> > > > >
> > > > >
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > > mutable std::vector <double> Aa;
> > > > > mutable std::vector <double> Af;
> > > > >
> > > > >
> > > > >
> > > > > /// Tabulate the regular entities of tensor for the contribution from a local cell
> > > > > virtual void tabulate_regular_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_0_cell_integral_0(const std::vector<const pum::GenericPUM*>& pums) : ufc::cell_integral(), pums(pums)
> > > > > {
> > > > > integral_0_quadrature = new poisson_0_cell_integral_0_quadrature(pums);
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_0_cell_integral_0()
> > > > > {
> > > > > delete integral_0_quadrature;
> > > > > }
> > > > >
> > > > >
> > > > > /// Tabulate the tensor for the contribution from a local cell
> > > > > virtual void tabulate_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const unsigned int num_entries = (3 + pums[0]->enriched_local_dimension(c))*(3 + pums[0]->enriched_local_dimension(c));
> > > > >
> > > > > for (unsigned int j = 0; j < num_entries; j++)
> > > > > A[j] = 0;
> > > > >
> > > > > // Add all contributions to element tensor
> > > > > integral_0_quadrature->tabulate_tensor(A, w, c);
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the assembly of the global
> > > > > /// tensor corresponding to a form with r + n arguments, that is, a
> > > > > /// mapping
> > > > > ///
> > > > > /// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
> > > > > ///
> > > > > /// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
> > > > > /// global tensor A is defined by
> > > > > ///
> > > > > /// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
> > > > > ///
> > > > > /// where each argument Vj represents the application to the
> > > > > /// sequence of basis functions of Vj and w1, w2, ..., wn are given
> > > > > /// fixed functions (coefficients).
> > > > >
> > > > > class poisson_form_0: public ufc::form
> > > > > {
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_form_0(const std::vector<const pum::GenericPUM*>& pums) : ufc::form(), pums(pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_form_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the form
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "Form([Integral(Product(Function(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 1), IndexSum(Product(Indexed(ComponentTensor(Sum(Indexed(SpatialDerivative(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 0), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((FixedIndex(0),), {})), Indexed(SpatialDerivative(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 0), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((FixedIndex(1),), {}))), MultiIndex((Index(0),), {Index(0): 2})), MultiIndex((Index(1),), {Index(1): 2})), Indexed(ComponentTensor(Sum(Indexed(SpatialDerivative(BasisFunction(MixedElement(*[FiniteElement('Lagrange', C
> ell(
> > > 'triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 1), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((FixedIndex(0),), {})), Indexed(SpatialDerivative(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 1), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((FixedIndex(1),), {}))), MultiIndex((Index(2),), {Index(2): 2})), MultiIndex((Index(1),), {Index(1): 2}))), MultiIndex((Index(1),), {Index(1): 2}))), Measure('cell', 0, None)), Integral(Product(Constant(Cell('triangle', 1, Space(2)), 0), Product(Indexed(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'va
> lue_
> > > shape': (2,) }), 0), MultiIndex((FixedIndex(1),), {FixedIndex(1): 2})), Indexed(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 1), MultiIndex((FixedIndex(1),), {FixedIndex(1): 2})))), Measure('surface', 0, None))])";
> > > > > }
> > > > >
> > > > > /// Return the rank of the global tensor (r)
> > > > > virtual unsigned int rank() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of coefficients (n)
> > > > > virtual unsigned int num_coefficients() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of cell integrals
> > > > > virtual unsigned int num_cell_integrals() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the number of exterior facet integrals
> > > > > virtual unsigned int num_exterior_facet_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the number of interior facet integrals
> > > > > virtual unsigned int num_interior_facet_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for argument function i
> > > > > virtual ufc::finite_element* create_finite_element(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_0_finite_element_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_0_finite_element_1();
> > > > > break;
> > > > > case 2:
> > > > > return new poisson_0_finite_element_2();
> > > > > break;
> > > > > case 3:
> > > > > return new poisson_0_finite_element_3();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new dof map for argument function i
> > > > > virtual ufc::dof_map* create_dof_map(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_0_dof_map_0(pums);
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_0_dof_map_1(pums);
> > > > > break;
> > > > > case 2:
> > > > > return new poisson_0_dof_map_2();
> > > > > break;
> > > > > case 3:
> > > > > return new poisson_0_dof_map_3();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new cell integral on sub domain i
> > > > > virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
> > > > > {
> > > > > return new poisson_0_cell_integral_0(pums);
> > > > > }
> > > > >
> > > > > /// Create a new exterior facet integral on sub domain i
> > > > > virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new interior facet integral on sub domain i
> > > > > virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_auxiliary_0_finite_element_0: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_auxiliary_0_finite_element_0() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_auxiliary_0_finite_element_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_auxiliary_0_finite_element_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_auxiliary_0_dof_map_0: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_auxiliary_0_dof_map_0() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_auxiliary_0_dof_map_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_auxiliary_0_dof_map_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the assembly of the global
> > > > > /// tensor corresponding to a form with r + n arguments, that is, a
> > > > > /// mapping
> > > > > ///
> > > > > /// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
> > > > > ///
> > > > > /// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
> > > > > /// global tensor A is defined by
> > > > > ///
> > > > > /// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
> > > > > ///
> > > > > /// where each argument Vj represents the application to the
> > > > > /// sequence of basis functions of Vj and w1, w2, ..., wn are given
> > > > > /// fixed functions (coefficients).
> > > > >
> > > > > class poisson_auxiliary_form_0: public ufc::form
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_auxiliary_form_0() : ufc::form()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_auxiliary_form_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the form
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "Auxiliary ufc::form to initialize standard functions, apply boundary conditions and obtain ufc::dof_map objects for continuous space(required for PUM objects) for a form containing discontinuous spaces.";
> > > > > }
> > > > >
> > > > > /// Return the rank of the global tensor (r)
> > > > > virtual unsigned int rank() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of coefficients (n)
> > > > > virtual unsigned int num_coefficients() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the number of cell integrals
> > > > > virtual unsigned int num_cell_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the number of exterior facet integrals
> > > > > virtual unsigned int num_exterior_facet_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the number of interior facet integrals
> > > > > virtual unsigned int num_interior_facet_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for argument function i
> > > > > virtual ufc::finite_element* create_finite_element(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_auxiliary_0_finite_element_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_auxiliary_0_finite_element_0();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new dof map for argument function i
> > > > > virtual ufc::dof_map* create_dof_map(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_auxiliary_0_dof_map_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_auxiliary_0_dof_map_0();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new cell integral on sub domain i
> > > > > virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new exterior facet integral on sub domain i
> > > > > virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new interior facet integral on sub domain i
> > > > > virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_1_finite_element_0_0: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_finite_element_0_0() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_finite_element_0_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_finite_element_0_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_1_finite_element_0_1: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_finite_element_0_1() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_finite_element_0_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_finite_element_0_1();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_1_finite_element_0: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_finite_element_0() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_finite_element_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 6;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > values[0] = 0;
> > > > > values[1] = 0;
> > > > >
> > > > > if (0 <= i && i <= 2)
> > > > > {
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > values[0] = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > if (3 <= i && i <= 5)
> > > > > {
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i - 3;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > values[1] = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 2*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > if (0 <= i && i <= 2)
> > > > > {
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > if (3 <= i && i <= 5)
> > > > > {
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i - 3;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[num_derivatives + row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[6][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}, {{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[6][1] = {{1}, {1}, {1}, {1}, {1}, {1}};
> > > > > static const double D[6][1][2] = {{{1, 0}}, {{1, 0}}, {{1, 0}}, {{0, 1}}, {{0, 1}}, {{0, 1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[2];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 2; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[2] = dof_values[1];
> > > > > vertex_values[4] = dof_values[2];
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[1] = dof_values[3];
> > > > > vertex_values[3] = dof_values[4];
> > > > > vertex_values[5] = dof_values[5];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_1_finite_element_0_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_1_finite_element_0_1();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_1_finite_element_1: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_finite_element_1() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_finite_element_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_finite_element_1();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_1_finite_element_2: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_finite_element_2() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_finite_element_2()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_finite_element_2();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_1_dof_map_0_0: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_dof_map_0_0() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_1_dof_map_0_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_dof_map_0_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_1_dof_map_0_1: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_dof_map_0_1(const std::vector<const pum::GenericPUM*>& pums) :ufc::dof_map(), pums(pums)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_1_dof_map_0_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension + pums[0]->enriched_global_dimension();
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return pums[0]->enriched_local_dimension(c);
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return pums[0]->enriched_max_local_dimension();
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Generate code for tabulating extra degrees of freedom.
> > > > > unsigned int local_offset = 0;
> > > > > unsigned int global_offset = 0;
> > > > >
> > > > > // Calculate local-to-global mapping for the enriched dofs related to the discontinuous field 0
> > > > > pums[0]->tabulate_enriched_dofs(dofs, c, local_offset, global_offset);
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > const std::vector<const pum::GenericPUM*>& p0 = boost::assign::list_of(pums[0]);
> > > > >
> > > > > return new poisson_1_dof_map_0_1(p0);
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_1_dof_map_0: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_dof_map_0(const std::vector<const pum::GenericPUM*>& pums) :ufc::dof_map(), pums(pums)
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_1_dof_map_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension + pums[0]->enriched_global_dimension();
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3 + pums[0]->enriched_local_dimension(c);
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3 + pums[0]->enriched_max_local_dimension();
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 4;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];\
> > > > >
> > > > > // Generate code for tabulating extra degrees of freedom.
> > > > > unsigned int local_offset = 3;
> > > > > unsigned int global_offset = m.num_entities[0];
> > > > >
> > > > > // Calculate local-to-global mapping for the enriched dofs related to the discontinuous field 0
> > > > > pums[0]->tabulate_enriched_dofs(dofs, c, local_offset, global_offset);
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > dofs[2] = 4;
> > > > > dofs[3] = 5;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > dofs[2] = 3;
> > > > > dofs[3] = 5;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > dofs[2] = 3;
> > > > > dofs[3] = 4;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > coordinates[3][0] = x[0][0];
> > > > > coordinates[3][1] = x[0][1];
> > > > > coordinates[4][0] = x[1][0];
> > > > > coordinates[4][1] = x[1][1];
> > > > > coordinates[5][0] = x[2][0];
> > > > > coordinates[5][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > const std::vector<const pum::GenericPUM*>& p1 = boost::assign::list_of(pums[0]);
> > > > >
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_1_dof_map_0_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_1_dof_map_0_1(p1);
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_1_dof_map_1: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_dof_map_1() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_1_dof_map_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_dof_map_1();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_1_dof_map_2: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_dof_map_2() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_1_dof_map_2()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_dof_map_2();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the tabulation of the cell
> > > > > /// tensor corresponding to the local contribution to a form from
> > > > > /// the integral over a cell.
> > > > >
> > > > > class poisson_1_cell_integral_0_quadrature: public ufc::cell_integral
> > > > > {
> > > > >
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > > mutable std::vector <double> Aa;
> > > > > mutable std::vector <double> Af;
> > > > >
> > > > >
> > > > >
> > > > > /// Tabulate the regular entities of tensor for the contribution from a local cell
> > > > > virtual void tabulate_regular_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * x = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = x[1][0] - x[0][0];
> > > > > const double J_01 = x[2][0] - x[0][0];
> > > > > const double J_10 = x[1][1] - x[0][1];
> > > > > const double J_11 = x[2][1] - x[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Set scale factor
> > > > > const double det = std::abs(detJ);
> > > > >
> > > > >
> > > > > // Array of quadrature weights
> > > > > static const double W4[4] = {0.159020690871988, 0.0909793091280112, 0.159020690871988, 0.0909793091280112};
> > > > > // Quadrature points on the UFC reference element: (0.178558728263616, 0.155051025721682), (0.0750311102226081, 0.644948974278318), (0.666390246014701, 0.155051025721682), (0.280019915499074, 0.644948974278318)
> > > > >
> > > > > // Value of basis functions at quadrature points.
> > > > > static const double FE0[4][3] = \
> > > > > {{0.666390246014701, 0.178558728263616, 0.155051025721682},
> > > > > {0.280019915499074, 0.0750311102226081, 0.644948974278318},
> > > > > {0.178558728263616, 0.666390246014701, 0.155051025721682},
> > > > > {0.0750311102226081, 0.280019915499074, 0.644948974278318}};
> > > > >
> > > > > static const double FE1_C0[4][6] = \
> > > > > {{0.666390246014701, 0.178558728263616, 0.155051025721682, 0, 0, 0},
> > > > > {0.280019915499074, 0.0750311102226081, 0.644948974278318, 0, 0, 0},
> > > > > {0.178558728263616, 0.666390246014701, 0.155051025721682, 0, 0, 0},
> > > > > {0.0750311102226081, 0.280019915499074, 0.644948974278318, 0, 0, 0}};
> > > > >
> > > > > static const double FE1_C1[4][6] = \
> > > > > {{0, 0, 0, 0.666390246014701, 0.178558728263616, 0.155051025721682},
> > > > > {0, 0, 0, 0.280019915499074, 0.0750311102226081, 0.644948974278318},
> > > > > {0, 0, 0, 0.178558728263616, 0.666390246014701, 0.155051025721682},
> > > > > {0, 0, 0, 0.0750311102226081, 0.280019915499074, 0.644948974278318}};
> > > > >
> > > > >
> > > > > // local dimension of the current cell
> > > > > unsigned int offset = 3 + pums[0]->enriched_local_dimension(c);
> > > > >
> > > > >
> > > > > // Remove regular local dimension to obtain number of enriched dofs
> > > > > offset -= 3;
> > > > >
> > > > > // Compute element tensor using UFL quadrature representation
> > > > > // Optimisations: ('simplify expressions', False), ('ignore zero tables', False), ('non zero columns', False), ('remove zero terms', False), ('ignore ones', False)
> > > > > // Total number of operations to compute element tensor: 144
> > > > >
> > > > > // Loop quadrature points for integral
> > > > > // Number of operations to compute element tensor for following IP loop = 144
> > > > > for (unsigned int ip = 0; ip < 4; ip++)
> > > > > {
> > > > >
> > > > > // Function declarations
> > > > > double F0 = 0;
> > > > >
> > > > > // Total number of operations to compute function values = 6
> > > > > for (unsigned int r = 0; r < 3; r++)
> > > > > {
> > > > > F0 += FE0[ip][r]*w[0][r];
> > > > > }// end loop over 'r'
> > > > > unsigned int m = 0;
> > > > >
> > > > > // Number of operations for primary indices = 30
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > if ((((0 <= j && j < 3))))
> > > > > {
> > > > > // Number of operations to compute entry = 5
> > > > > A[m] += (FE1_C0[ip][j] + FE1_C1[ip][j])*F0*W4[ip]*det;
> > > > >
> > > > > ++m;
> > > > > }
> > > > > }// end loop over 'j'
> > > > > }// end loop over 'ip'
> > > > > }
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_cell_integral_0_quadrature(const std::vector<const pum::GenericPUM*>& pums) : ufc::cell_integral(), pums(pums)
> > > > > {
> > > > > //Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_cell_integral_0_quadrature()
> > > > > {
> > > > > //Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > /// Tabulate the tensor for the contribution from a local cell
> > > > > virtual void tabulate_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Tabulate regular entires of element tensor
> > > > > tabulate_regular_tensor(A, w, c);
> > > > >
> > > > > // local dimension of the current cell
> > > > > unsigned int num_entries = 3 + pums[0]->enriched_local_dimension(c);
> > > > >
> > > > >
> > > > > // Remove regular local dimension to obtain number of enriched dofs
> > > > > num_entries -= 3;
> > > > >
> > > > > if (num_entries == 0)
> > > > > return;
> > > > >
> > > > >
> > > > > // Extract vertex coordinates
> > > > > const double * const * x = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = x[1][0] - x[0][0];
> > > > > const double J_01 = x[2][0] - x[0][0];
> > > > > const double J_10 = x[1][1] - x[0][1];
> > > > > const double J_11 = x[2][1] - x[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > >
> > > > > // Set scale factor
> > > > > const double det = std::abs(detJ);
> > > > >
> > > > > // FIXME: It will crash for multiple discontinuities, if we don't have at least one cell which all dofs are enriched
> > > > > const unsigned int min_entries = 6;
> > > > > const unsigned int _num_entries = std::max(num_entries, min_entries);
> > > > >
> > > > > // Resizing and reseting auxiliary tensors
> > > > > Aa.resize(_num_entries);
> > > > > std::fill(Aa.begin(), Aa.end(), 0.0);
> > > > >
> > > > > // Define an array to save current quadrature point
> > > > > double coordinate[2];
> > > > >
> > > > > // Define ufc::finite_element object(s) to evalaute shape functions or their derivatives on runtime
> > > > > poisson_1_finite_element_1 element_0;
> > > > > poisson_1_finite_element_0 element_1;
> > > > >
> > > > > // Array of quadrature weights
> > > > > static const double W4[4] = {0.159020690871988, 0.0909793091280112, 0.159020690871988, 0.0909793091280112};
> > > > >
> > > > >
> > > > > // Array of quadrature points
> > > > > static const double P4[8] = \
> > > > > {0.178558728263616, 0.155051025721682,
> > > > > 0.0750311102226081, 0.644948974278318,
> > > > > 0.666390246014701, 0.155051025721682,
> > > > > 0.280019915499074, 0.644948974278318};
> > > > >
> > > > > // Define vectors for quadrature points and weights(note that the sizes are determined in compile time)
> > > > > std::vector <double> Wn4;
> > > > > std::vector <double> Pn4;
> > > > >
> > > > >
> > > > > // Check whether there is any need to use modified integration scheme
> > > > > if ((pums[0]->modified_quadrature(c)))
> > > > > {
> > > > >
> > > > > const std::vector<double> weight4(W4, W4 + 4);
> > > > > const std::vector<double> point4(P4, P4 + 8);
> > > > >
> > > > > ConstQuadratureRule standard_gauss = std::make_pair(point4, weight4);
> > > > > QuadratureRule modified_gauss;
> > > > >
> > > > > pums[0]->cell_quadrature_rule(modified_gauss, standard_gauss, c);
> > > > >
> > > > > Pn4 = modified_gauss.first;
> > > > > Wn4 = modified_gauss.second;
> > > > >
> > > > > }
> > > > > else
> > > > > {
> > > > > // Map quadrature points from the reference cell to the physical cell
> > > > > Wn4.resize(4);;
> > > > > Pn4.resize(8);;
> > > > >
> > > > >
> > > > > for (unsigned int i = 0; i < 4; i++)
> > > > > {
> > > > > Wn4[i] = W4[i];
> > > > > for (unsigned int j = 0; j < 2; j++)
> > > > > Pn4[2*i + j] = x[0][j]*(1.0 - P4[2*i] - P4[2*i + 1]) + x[1][j]*P4[2*i + 1] + x[2][j]*P4[2*i];
> > > > > }
> > > > > }
> > > > >
> > > > >
> > > > > // Return the values of enriched function at the quadrature points
> > > > > std::vector<double> enriched_values_4;
> > > > > pums[0]->tabulate_enriched_basis(enriched_values_4, Pn4, c);
> > > > >
> > > > > // Define an auxilary index: m
> > > > > unsigned int m = 0;
> > > > >
> > > > >
> > > > > // Loop over new quadrature points for integral
> > > > > for (unsigned int ip = 0; ip < Wn4.size(); ip++)
> > > > > {
> > > > > // Evalaute tables and entries in the element tensor, if the enhanced value at this quadrature point is non-zero
> > > > > if (enriched_values_4[ip] != 0)
> > > > > {
> > > > > // Pick up the coordinates of the current quadrature point
> > > > > coordinate[0] = Pn4[2*ip];
> > > > > coordinate[1] = Pn4[2*ip + 1];
> > > > >
> > > > >
> > > > > // Creating a table to save the values of shape functions at the current guass point for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)
> > > > > double value_0[1];
> > > > > double table_0_D0[3][1];
> > > > > for (unsigned int j = 0; j < 3; j++)
> > > > > {
> > > > > element_0.evaluate_basis(j, value_0, coordinate, c);
> > > > > for (unsigned int k = 0; k < 1; k++)
> > > > > table_0_D0[j][k] = value_0[k];
> > > > > }
> > > > >
> > > > >
> > > > > // Creating a table to save the values of shape functions at the current guass point for MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })
> > > > > double value_1[2];
> > > > > double table_1_D0[6][2];
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > element_1.evaluate_basis(j, value_1, coordinate, c);
> > > > > for (unsigned int k = 0; k < 2; k++)
> > > > > table_1_D0[j][k] = value_1[k];
> > > > > }
> > > > >
> > > > > // Function declarations
> > > > > double F0 = 0;
> > > > >
> > > > > // Total number of operations to compute function values = 6
> > > > > for (unsigned int r = 0; r < 3; r++)
> > > > > {
> > > > > F0 += table_0_D0[r][0]*w[0][r];
> > > > > }// end loop over 'r'
> > > > >
> > > > > // Number of operations for primary indices = 30
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > if (!(((0 <= j && j < 3))))
> > > > > {
> > > > > // Move the indices of discontinuous spaces to the end of mixed space
> > > > > if ((3 <= j && j < 6))
> > > > > {
> > > > > m = j;
> > > > > }
> > > > > // Number of operations to compute entry = 5
> > > > > Aa[m] += (table_1_D0[j][0] + table_1_D0[j][1])*F0*Wn4[ip]*det;
> > > > > }// end check for enriched entiries
> > > > > }// end loop over 'j'
> > > > > }
> > > > > }// end loop over 'ip'
> > > > >
> > > > >
> > > > > // Pick up entries from the total element tensor for the nodes active in the enrichment
> > > > >
> > > > > // Determine a vector that contains the local numbering of enriched degrees of freedom in ufc::cell c for the field 0
> > > > > std::vector<unsigned int> active_dofs_0;
> > > > > pums[0]->tabulate_enriched_local_dofs(active_dofs_0, c);
> > > > > std::vector<unsigned int>::iterator it_0_0;
> > > > >
> > > > >
> > > > > m = 0;
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > if ((0 <= j && j < 3))
> > > > > ++m;
> > > > > else
> > > > > {
> > > > > it_0_0 = find(active_dofs_0.begin(), active_dofs_0.end(), j - 3);
> > > > >
> > > > >
> > > > > // Check whether the entry is coressponding to the active enriched node
> > > > > if (it_0_0 != active_dofs_0.end())
> > > > > {
> > > > > A[m] = Aa[j];
> > > > > ++m;
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the tabulation of the cell
> > > > > /// tensor corresponding to the local contribution to a form from
> > > > > /// the integral over a cell.
> > > > >
> > > > > class poisson_1_cell_integral_0: public ufc::cell_integral
> > > > > {
> > > > > private:
> > > > >
> > > > > poisson_1_cell_integral_0_quadrature* integral_0_quadrature;
> > > > >
> > > > >
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > > mutable std::vector <double> Aa;
> > > > > mutable std::vector <double> Af;
> > > > >
> > > > >
> > > > >
> > > > > /// Tabulate the regular entities of tensor for the contribution from a local cell
> > > > > virtual void tabulate_regular_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_cell_integral_0(const std::vector<const pum::GenericPUM*>& pums) : ufc::cell_integral(), pums(pums)
> > > > > {
> > > > > integral_0_quadrature = new poisson_1_cell_integral_0_quadrature(pums);
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_cell_integral_0()
> > > > > {
> > > > > delete integral_0_quadrature;
> > > > > }
> > > > >
> > > > >
> > > > > /// Tabulate the tensor for the contribution from a local cell
> > > > > virtual void tabulate_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const unsigned int num_entries = (3 + pums[0]->enriched_local_dimension(c));
> > > > >
> > > > > for (unsigned int j = 0; j < num_entries; j++)
> > > > > A[j] = 0;
> > > > >
> > > > > // Add all contributions to element tensor
> > > > > integral_0_quadrature->tabulate_tensor(A, w, c);
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the tabulation of the
> > > > > /// exterior facet tensor corresponding to the local contribution to
> > > > > /// a form from the integral over an exterior facet.
> > > > >
> > > > > class poisson_1_exterior_facet_integral_0_quadrature: public ufc::exterior_facet_integral
> > > > > {
> > > > >
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > > mutable std::vector <double> Aa;
> > > > > mutable std::vector <double> Af;
> > > > >
> > > > >
> > > > >
> > > > > /// Tabulate the regular entities of the tensor for the contribution from a local exterior facet
> > > > > virtual void tabulate_regular_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c,
> > > > > unsigned int facet) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * x = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Vertices on edges
> > > > > static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
> > > > >
> > > > > // Get vertices
> > > > > const unsigned int v0 = edge_vertices[facet][0];
> > > > > const unsigned int v1 = edge_vertices[facet][1];
> > > > >
> > > > > // Compute scale factor (length of edge scaled by length of reference interval)
> > > > > const double dx0 = x[v1][0] - x[v0][0];
> > > > > const double dx1 = x[v1][1] - x[v0][1];
> > > > > const double det = std::sqrt(dx0*dx0 + dx1*dx1);
> > > > >
> > > > >
> > > > > // Compute facet normals from the facet scale factor constants
> > > > >
> > > > >
> > > > > // Array of quadrature weights
> > > > > static const double W2[2] = {0.5, 0.5};
> > > > > // Quadrature points on the UFC reference element: (0.211324865405187), (0.788675134594813)
> > > > >
> > > > > // Value of basis functions at quadrature points.
> > > > > static const double FE0_f0[2][3] = \
> > > > > {{0, 0.788675134594813, 0.211324865405187},
> > > > > {0, 0.211324865405187, 0.788675134594813}};
> > > > >
> > > > > static const double FE0_f1[2][3] = \
> > > > > {{0.788675134594813, 0, 0.211324865405187},
> > > > > {0.211324865405187, 0, 0.788675134594813}};
> > > > >
> > > > > static const double FE0_f2[2][3] = \
> > > > > {{0.788675134594813, 0.211324865405187, 0},
> > > > > {0.211324865405187, 0.788675134594813, 0}};
> > > > >
> > > > > static const double FE1_f0_C0[2][6] = \
> > > > > {{0, 0.788675134594813, 0.211324865405187, 0, 0, 0},
> > > > > {0, 0.211324865405187, 0.788675134594813, 0, 0, 0}};
> > > > >
> > > > > static const double FE1_f0_C1[2][6] = \
> > > > > {{0, 0, 0, 0, 0.788675134594813, 0.211324865405187},
> > > > > {0, 0, 0, 0, 0.211324865405187, 0.788675134594813}};
> > > > >
> > > > > static const double FE1_f1_C0[2][6] = \
> > > > > {{0.788675134594813, 0, 0.211324865405187, 0, 0, 0},
> > > > > {0.211324865405187, 0, 0.788675134594813, 0, 0, 0}};
> > > > >
> > > > > static const double FE1_f1_C1[2][6] = \
> > > > > {{0, 0, 0, 0.788675134594813, 0, 0.211324865405187},
> > > > > {0, 0, 0, 0.211324865405187, 0, 0.788675134594813}};
> > > > >
> > > > > static const double FE1_f2_C0[2][6] = \
> > > > > {{0.788675134594813, 0.211324865405187, 0, 0, 0, 0},
> > > > > {0.211324865405187, 0.788675134594813, 0, 0, 0, 0}};
> > > > >
> > > > > static const double FE1_f2_C1[2][6] = \
> > > > > {{0, 0, 0, 0.788675134594813, 0.211324865405187, 0},
> > > > > {0, 0, 0, 0.211324865405187, 0.788675134594813, 0}};
> > > > >
> > > > >
> > > > > // local dimension of the current cell
> > > > > unsigned int offset = 3 + pums[0]->enriched_local_dimension(c);
> > > > >
> > > > >
> > > > > // Remove regular local dimension to obtain number of enriched dofs
> > > > > offset -= 3;
> > > > >
> > > > > // Compute element tensor using UFL quadrature representation
> > > > > // Optimisations: ('simplify expressions', False), ('ignore zero tables', False), ('non zero columns', False), ('remove zero terms', False), ('ignore ones', False)
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > {
> > > > > // Total number of operations to compute element tensor (from this point): 84
> > > > >
> > > > > // Loop quadrature points for integral
> > > > > // Number of operations to compute element tensor for following IP loop = 84
> > > > > for (unsigned int ip = 0; ip < 2; ip++)
> > > > > {
> > > > >
> > > > > // Function declarations
> > > > > double F0 = 0;
> > > > >
> > > > > // Total number of operations to compute function values = 6
> > > > > for (unsigned int r = 0; r < 3; r++)
> > > > > {
> > > > > F0 += FE0_f0[ip][r]*w[1][r];
> > > > > }// end loop over 'r'
> > > > > unsigned int m = 0;
> > > > >
> > > > > // Number of operations for primary indices = 36
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > if ((((0 <= j && j < 3))))
> > > > > {
> > > > > // Number of operations to compute entry = 6
> > > > > A[m] += (FE1_f0_C0[ip][j] + FE1_f0_C1[ip][j])*F0*-1*W2[ip]*det;
> > > > >
> > > > > ++m;
> > > > > }
> > > > > }// end loop over 'j'
> > > > > }// end loop over 'ip'
> > > > > }
> > > > > break;
> > > > > case 1:
> > > > > {
> > > > > // Total number of operations to compute element tensor (from this point): 84
> > > > >
> > > > > // Loop quadrature points for integral
> > > > > // Number of operations to compute element tensor for following IP loop = 84
> > > > > for (unsigned int ip = 0; ip < 2; ip++)
> > > > > {
> > > > >
> > > > > // Function declarations
> > > > > double F0 = 0;
> > > > >
> > > > > // Total number of operations to compute function values = 6
> > > > > for (unsigned int r = 0; r < 3; r++)
> > > > > {
> > > > > F0 += FE0_f1[ip][r]*w[1][r];
> > > > > }// end loop over 'r'
> > > > > unsigned int m = 0;
> > > > >
> > > > > // Number of operations for primary indices = 36
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > if ((((0 <= j && j < 3))))
> > > > > {
> > > > > // Number of operations to compute entry = 6
> > > > > A[m] += (FE1_f1_C0[ip][j] + FE1_f1_C1[ip][j])*F0*-1*W2[ip]*det;
> > > > >
> > > > > ++m;
> > > > > }
> > > > > }// end loop over 'j'
> > > > > }// end loop over 'ip'
> > > > > }
> > > > > break;
> > > > > case 2:
> > > > > {
> > > > > // Total number of operations to compute element tensor (from this point): 84
> > > > >
> > > > > // Loop quadrature points for integral
> > > > > // Number of operations to compute element tensor for following IP loop = 84
> > > > > for (unsigned int ip = 0; ip < 2; ip++)
> > > > > {
> > > > >
> > > > > // Function declarations
> > > > > double F0 = 0;
> > > > >
> > > > > // Total number of operations to compute function values = 6
> > > > > for (unsigned int r = 0; r < 3; r++)
> > > > > {
> > > > > F0 += FE0_f2[ip][r]*w[1][r];
> > > > > }// end loop over 'r'
> > > > > unsigned int m = 0;
> > > > >
> > > > > // Number of operations for primary indices = 36
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > if ((((0 <= j && j < 3))))
> > > > > {
> > > > > // Number of operations to compute entry = 6
> > > > > A[m] += (FE1_f2_C1[ip][j] + FE1_f2_C0[ip][j])*F0*-1*W2[ip]*det;
> > > > >
> > > > > ++m;
> > > > > }
> > > > > }// end loop over 'j'
> > > > > }// end loop over 'ip'
> > > > > }
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_exterior_facet_integral_0_quadrature(const std::vector<const pum::GenericPUM*>& pums) : ufc::exterior_facet_integral(), pums(pums)
> > > > > {
> > > > > //Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_exterior_facet_integral_0_quadrature()
> > > > > {
> > > > > //Do nothing
> > > > > }
> > > > >
> > > > > /// Tabulate the tensor for the contribution from a local exterior facet
> > > > > virtual void tabulate_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c,
> > > > > unsigned int facet) const
> > > > > {
> > > > > // Tabulate regular entires of element tensor
> > > > > tabulate_regular_tensor(A, w, c, facet);
> > > > >
> > > > > // local dimension of the current cell
> > > > > unsigned int num_entries = 3 + pums[0]->enriched_local_dimension(c);
> > > > >
> > > > >
> > > > > // Remove regular local dimension to obtain number of enriched dofs
> > > > > num_entries -= 3;
> > > > >
> > > > > if (num_entries == 0)
> > > > > return;
> > > > >
> > > > >
> > > > > // Extract vertex coordinates
> > > > > const double * const * x = c.coordinates;
> > > > >
> > > > > // Vertices on edges
> > > > > static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
> > > > >
> > > > > // Get vertices
> > > > > const unsigned int v0 = edge_vertices[facet][0];
> > > > > const unsigned int v1 = edge_vertices[facet][1];
> > > > >
> > > > > // Compute scale factor (length of edge scaled by length of reference interval)
> > > > > const double dx0 = x[v1][0] - x[v0][0];
> > > > > const double dx1 = x[v1][1] - x[v0][1];
> > > > > const double det = std::sqrt(dx0*dx0 + dx1*dx1);
> > > > >
> > > > >
> > > > > // Compute facet normals from the facet scale factor constants
> > > > >
> > > > > // FIXME: It will crash for multiple discontinuities, if we don't have at least one cell which all dofs are enriched
> > > > > const unsigned int min_entries = 6;
> > > > > const unsigned int _num_entries = std::max(num_entries, min_entries);
> > > > >
> > > > > // Resizing and reseting auxiliary tensors
> > > > > Aa.resize(_num_entries);
> > > > > std::fill(Aa.begin(), Aa.end(), 0.0);
> > > > >
> > > > > // Define an array to save current quadrature point
> > > > > double coordinate[2];
> > > > >
> > > > > // Define ufc::finite_element object(s) to evalaute shape functions or their derivatives on runtime
> > > > > poisson_1_finite_element_1 element_0;
> > > > > poisson_1_finite_element_0 element_1;
> > > > >
> > > > > // Array of quadrature weights
> > > > > static const double W2[2] = {0.5, 0.5};
> > > > >
> > > > >
> > > > > // Array of quadrature points
> > > > > static const double P2[2] = \
> > > > > {0.211324865405187,
> > > > > 0.788675134594813};
> > > > >
> > > > > // Define vectors for quadrature points and weights(note that the sizes are determined in compile time)
> > > > > std::vector <double> Wn2;
> > > > > std::vector <double> Pn2;
> > > > >
> > > > >
> > > > > // Check whether there is any need to use modified integration scheme
> > > > > if ((pums[0]->modified_quadrature(c, facet)))
> > > > > {
> > > > >
> > > > > const std::vector<double> weight2(W2, W2 + 2);
> > > > > const std::vector<double> point2(P2, P2 + 2);
> > > > >
> > > > > ConstQuadratureRule standard_gauss = std::make_pair(point2, weight2);
> > > > > QuadratureRule modified_gauss;
> > > > >
> > > > > pums[0]->facet_quadrature_rule(modified_gauss, standard_gauss, c, facet);
> > > > >
> > > > > Pn2 = modified_gauss.first;
> > > > > Wn2 = modified_gauss.second;
> > > > >
> > > > > }
> > > > > else
> > > > > {
> > > > > // Map quadrature points from the reference cell to the physical cell
> > > > > Wn2.resize(2);;
> > > > > Pn2.resize(4);;
> > > > >
> > > > >
> > > > > for (unsigned int i = 0; i < 2; i++)
> > > > > {
> > > > > Wn2[i] = W2[i];
> > > > > for (unsigned int j = 0; j < 2; j++)
> > > > > Pn2[2*i + j] = x[v0][j]*(1.0 - P2[i]) + x[v1][j]*P2[i];
> > > > > }
> > > > > }
> > > > >
> > > > >
> > > > > // Return the values of enriched function at the quadrature points
> > > > > std::vector<double> enriched_values_2;
> > > > > pums[0]->tabulate_enriched_basis(enriched_values_2, Pn2, c);
> > > > >
> > > > > // Define an auxilary index: m
> > > > > unsigned int m = 0;
> > > > >
> > > > >
> > > > > // Loop over new quadrature points for integral
> > > > > for (unsigned int ip = 0; ip < Wn2.size(); ip++)
> > > > > {
> > > > > // Evalaute tables and entries in the element tensor, if the enhanced value at this quadrature point is non-zero
> > > > > if (enriched_values_2[ip] != 0)
> > > > > {
> > > > > // Pick up the coordinates of the current quadrature point
> > > > > coordinate[0] = Pn2[2*ip];
> > > > > coordinate[1] = Pn2[2*ip + 1];
> > > > >
> > > > >
> > > > > // Creating a table to save the values of shape functions at the current guass point for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)
> > > > > double value_0[1];
> > > > > double table_0_D0[3][1];
> > > > > for (unsigned int j = 0; j < 3; j++)
> > > > > {
> > > > > element_0.evaluate_basis(j, value_0, coordinate, c);
> > > > > for (unsigned int k = 0; k < 1; k++)
> > > > > table_0_D0[j][k] = value_0[k];
> > > > > }
> > > > >
> > > > >
> > > > > // Creating a table to save the values of shape functions at the current guass point for MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })
> > > > > double value_1[2];
> > > > > double table_1_D0[6][2];
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > element_1.evaluate_basis(j, value_1, coordinate, c);
> > > > > for (unsigned int k = 0; k < 2; k++)
> > > > > table_1_D0[j][k] = value_1[k];
> > > > > }
> > > > >
> > > > > // Function declarations
> > > > > double F0 = 0;
> > > > >
> > > > > // Total number of operations to compute function values = 6
> > > > > for (unsigned int r = 0; r < 3; r++)
> > > > > {
> > > > > F0 += table_0_D0[r][0]*w[1][r];
> > > > > }// end loop over 'r'
> > > > >
> > > > > // Number of operations for primary indices = 36
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > {
> > > > > if (!(((0 <= j && j < 3))))
> > > > > {
> > > > > // Move the indices of discontinuous spaces to the end of mixed space
> > > > > if ((3 <= j && j < 6))
> > > > > {
> > > > > m = j;
> > > > > }
> > > > > // Number of operations to compute entry = 6
> > > > > Aa[m] += (table_1_D0[j][0] + table_1_D0[j][1])*F0*-1*Wn2[ip]*det;
> > > > > }// end check for enriched entiries
> > > > > }// end loop over 'j'
> > > > > }
> > > > > }// end loop over 'ip'
> > > > >
> > > > >
> > > > > // Pick up entries from the total element tensor for the nodes active in the enrichment
> > > > >
> > > > > // Determine a vector that contains the local numbering of enriched degrees of freedom in ufc::cell c for the field 0
> > > > > std::vector<unsigned int> active_dofs_0;
> > > > > pums[0]->tabulate_enriched_local_dofs(active_dofs_0, c);
> > > > > std::vector<unsigned int>::iterator it_0_0;
> > > > >
> > > > >
> > > > > m = 0;
> > > > > for (unsigned int j = 0; j < 6; j++)
> > > > > if ((0 <= j && j < 3))
> > > > > ++m;
> > > > > else
> > > > > {
> > > > > it_0_0 = find(active_dofs_0.begin(), active_dofs_0.end(), j - 3);
> > > > >
> > > > >
> > > > > // Check whether the entry is coressponding to the active enriched node
> > > > > if (it_0_0 != active_dofs_0.end())
> > > > > {
> > > > > A[m] = Aa[j];
> > > > > ++m;
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the tabulation of the
> > > > > /// exterior facet tensor corresponding to the local contribution to
> > > > > /// a form from the integral over an exterior facet.
> > > > >
> > > > > class poisson_1_exterior_facet_integral_0: public ufc::exterior_facet_integral
> > > > > {
> > > > > private:
> > > > >
> > > > > poisson_1_exterior_facet_integral_0_quadrature* integral_0_quadrature;
> > > > >
> > > > >
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > > mutable std::vector <double> Aa;
> > > > > mutable std::vector <double> Af;
> > > > >
> > > > >
> > > > >
> > > > > /// Tabulate the regular entities of the tensor for the contribution from a local exterior facet
> > > > > virtual void tabulate_regular_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c,
> > > > > unsigned int facet) const
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_1_exterior_facet_integral_0(const std::vector<const pum::GenericPUM*>& pums) : ufc::exterior_facet_integral(), pums(pums)
> > > > > {
> > > > > integral_0_quadrature = new poisson_1_exterior_facet_integral_0_quadrature(pums);
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_1_exterior_facet_integral_0()
> > > > > {
> > > > > delete integral_0_quadrature;
> > > > > }
> > > > >
> > > > > /// Tabulate the tensor for the contribution from a local exterior facet
> > > > > virtual void tabulate_tensor(double* A,
> > > > > const double * const * w,
> > > > > const ufc::cell& c,
> > > > > unsigned int facet) const
> > > > > {
> > > > > const unsigned int num_entries = (3 + pums[0]->enriched_local_dimension(c));
> > > > >
> > > > > for (unsigned int j = 0; j < num_entries; j++)
> > > > > A[j] = 0;
> > > > >
> > > > > // Add all contributions to element tensor
> > > > > integral_0_quadrature->tabulate_tensor(A, w, c, facet);
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the assembly of the global
> > > > > /// tensor corresponding to a form with r + n arguments, that is, a
> > > > > /// mapping
> > > > > ///
> > > > > /// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
> > > > > ///
> > > > > /// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
> > > > > /// global tensor A is defined by
> > > > > ///
> > > > > /// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
> > > > > ///
> > > > > /// where each argument Vj represents the application to the
> > > > > /// sequence of basis functions of Vj and w1, w2, ..., wn are given
> > > > > /// fixed functions (coefficients).
> > > > >
> > > > > class poisson_form_1: public ufc::form
> > > > > {
> > > > > const std::vector<const pum::GenericPUM*>& pums;
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_form_1(const std::vector<const pum::GenericPUM*>& pums) : ufc::form(), pums(pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_form_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the form
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "Form([Integral(Product(Function(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 0), Sum(Indexed(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 0), MultiIndex((FixedIndex(0),), {FixedIndex(0): 2})), Indexed(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 0), MultiIndex((FixedIndex(1),), {FixedIndex(1): 2})))), Measure('cell', 0, None)), Integral(Product(IntValue(-1, (), (), {}), Product(Function(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), 1), Sum(Indexed(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1,
> Spa
> > > ce(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 0), MultiIndex((FixedIndex(0),), {FixedIndex(0): 2})), Indexed(BasisFunction(MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) }), 0), MultiIndex((FixedIndex(1),), {FixedIndex(1): 2}))))), Measure('exterior_facet', 0, None))])";
> > > > > }
> > > > >
> > > > > /// Return the rank of the global tensor (r)
> > > > > virtual unsigned int rank() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the number of coefficients (n)
> > > > > virtual unsigned int num_coefficients() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of cell integrals
> > > > > virtual unsigned int num_cell_integrals() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the number of exterior facet integrals
> > > > > virtual unsigned int num_exterior_facet_integrals() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the number of interior facet integrals
> > > > > virtual unsigned int num_interior_facet_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for argument function i
> > > > > virtual ufc::finite_element* create_finite_element(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_1_finite_element_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_1_finite_element_1();
> > > > > break;
> > > > > case 2:
> > > > > return new poisson_1_finite_element_2();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new dof map for argument function i
> > > > > virtual ufc::dof_map* create_dof_map(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_1_dof_map_0(pums);
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_1_dof_map_1();
> > > > > break;
> > > > > case 2:
> > > > > return new poisson_1_dof_map_2();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new cell integral on sub domain i
> > > > > virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_cell_integral_0(pums);
> > > > > }
> > > > >
> > > > > /// Create a new exterior facet integral on sub domain i
> > > > > virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
> > > > > {
> > > > > return new poisson_1_exterior_facet_integral_0(pums);
> > > > > }
> > > > >
> > > > > /// Create a new interior facet integral on sub domain i
> > > > > virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a finite element.
> > > > >
> > > > > class poisson_auxiliary_1_finite_element_0: public ufc::finite_element
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_auxiliary_1_finite_element_0() : ufc::finite_element()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_auxiliary_1_finite_element_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the finite element
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return the cell shape
> > > > > virtual ufc::shape cell_shape() const
> > > > > {
> > > > > return ufc::triangle;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the finite element function space
> > > > > virtual unsigned int space_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the rank of the value space
> > > > > virtual unsigned int value_rank() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the value space for axis i
> > > > > virtual unsigned int value_dimension(unsigned int i) const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Evaluate basis function i at given point in cell
> > > > > virtual void evaluate_basis(unsigned int i,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Reset values
> > > > > *values = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Extract relevant coefficients
> > > > > const double coeff0_0 = coefficients0[dof][0];
> > > > > const double coeff0_1 = coefficients0[dof][1];
> > > > > const double coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Compute value(s)
> > > > > *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > /// Evaluate all basis functions at given point in cell
> > > > > virtual void evaluate_basis_all(double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of basis function i at given point in cell
> > > > > virtual void evaluate_basis_derivatives(unsigned int i,
> > > > > unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Extract vertex coordinates
> > > > > const double * const * element_coordinates = c.coordinates;
> > > > >
> > > > > // Compute Jacobian of affine map from reference cell
> > > > > const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
> > > > > const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
> > > > > const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
> > > > > const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
> > > > >
> > > > > // Compute determinant of Jacobian
> > > > > const double detJ = J_00*J_11 - J_01*J_10;
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > >
> > > > > // Get coordinates and map to the reference (UFC) element
> > > > > double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
> > > > > element_coordinates[0][0]*element_coordinates[2][1] +\
> > > > > J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
> > > > > double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
> > > > > element_coordinates[1][0]*element_coordinates[0][1] -\
> > > > > J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
> > > > >
> > > > > // Map coordinates to the reference square
> > > > > if (std::abs(y - 1.0) < 1e-14)
> > > > > x = -1.0;
> > > > > else
> > > > > x = 2.0 *x/(1.0 - y) - 1.0;
> > > > > y = 2.0*y - 1.0;
> > > > >
> > > > > // Compute number of derivatives
> > > > > unsigned int num_derivatives = 1;
> > > > >
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > num_derivatives *= 2;
> > > > >
> > > > >
> > > > > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > > > > unsigned int **combinations = new unsigned int *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > combinations[j] = new unsigned int [n];
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > combinations[j][k] = 0;
> > > > > }
> > > > >
> > > > > // Generate combinations of derivatives
> > > > > for (unsigned int row = 1; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int num = 0; num < row; num++)
> > > > > {
> > > > > for (unsigned int col = n-1; col+1 > 0; col--)
> > > > > {
> > > > > if (combinations[row][col] + 1 > 1)
> > > > > combinations[row][col] = 0;
> > > > > else
> > > > > {
> > > > > combinations[row][col] += 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > > }
> > > > > }
> > > > >
> > > > > // Compute inverse of Jacobian
> > > > > const double Jinv[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
> > > > >
> > > > > // Declare transformation matrix
> > > > > // Declare pointer to two dimensional array and initialise
> > > > > double **transform = new double *[num_derivatives];
> > > > >
> > > > > for (unsigned int j = 0; j < num_derivatives; j++)
> > > > > {
> > > > > transform[j] = new double [num_derivatives];
> > > > > for (unsigned int k = 0; k < num_derivatives; k++)
> > > > > transform[j][k] = 1;
> > > > > }
> > > > >
> > > > > // Construct transformation matrix
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > for (unsigned int k = 0; k < n; k++)
> > > > > transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
> > > > > }
> > > > > }
> > > > >
> > > > > // Reset values
> > > > > for (unsigned int j = 0; j < 1*num_derivatives; j++)
> > > > > values[j] = 0;
> > > > >
> > > > > // Map degree of freedom to element degree of freedom
> > > > > const unsigned int dof = i;
> > > > >
> > > > > // Generate scalings
> > > > > const double scalings_y_0 = 1;
> > > > > const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
> > > > >
> > > > > // Compute psitilde_a
> > > > > const double psitilde_a_0 = 1;
> > > > > const double psitilde_a_1 = x;
> > > > >
> > > > > // Compute psitilde_bs
> > > > > const double psitilde_bs_0_0 = 1;
> > > > > const double psitilde_bs_0_1 = 1.5*y + 0.5;
> > > > > const double psitilde_bs_1_0 = 1;
> > > > >
> > > > > // Compute basisvalues
> > > > > const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
> > > > > const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
> > > > > const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
> > > > >
> > > > > // Table(s) of coefficients
> > > > > static const double coefficients0[3][3] = \
> > > > > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > > > > {0.471404520791032, 0, 0.333333333333333}};
> > > > >
> > > > > // Interesting (new) part
> > > > > // Tables of derivatives of the polynomial base (transpose)
> > > > > static const double dmats0[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {4.89897948556636, 0, 0},
> > > > > {0, 0, 0}};
> > > > >
> > > > > static const double dmats1[3][3] = \
> > > > > {{0, 0, 0},
> > > > > {2.44948974278318, 0, 0},
> > > > > {4.24264068711928, 0, 0}};
> > > > >
> > > > > // Compute reference derivatives
> > > > > // Declare pointer to array of derivatives on FIAT element
> > > > > double *derivatives = new double [num_derivatives];
> > > > >
> > > > > // Declare coefficients
> > > > > double coeff0_0 = 0;
> > > > > double coeff0_1 = 0;
> > > > > double coeff0_2 = 0;
> > > > >
> > > > > // Declare new coefficients
> > > > > double new_coeff0_0 = 0;
> > > > > double new_coeff0_1 = 0;
> > > > > double new_coeff0_2 = 0;
> > > > >
> > > > > // Loop possible derivatives
> > > > > for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
> > > > > {
> > > > > // Get values from coefficients array
> > > > > new_coeff0_0 = coefficients0[dof][0];
> > > > > new_coeff0_1 = coefficients0[dof][1];
> > > > > new_coeff0_2 = coefficients0[dof][2];
> > > > >
> > > > > // Loop derivative order
> > > > > for (unsigned int j = 0; j < n; j++)
> > > > > {
> > > > > // Update old coefficients
> > > > > coeff0_0 = new_coeff0_0;
> > > > > coeff0_1 = new_coeff0_1;
> > > > > coeff0_2 = new_coeff0_2;
> > > > >
> > > > > if(combinations[deriv_num][j] == 0)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
> > > > > }
> > > > > if(combinations[deriv_num][j] == 1)
> > > > > {
> > > > > new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
> > > > > new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
> > > > > new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
> > > > > }
> > > > >
> > > > > }
> > > > > // Compute derivatives on reference element as dot product of coefficients and basisvalues
> > > > > derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
> > > > > }
> > > > >
> > > > > // Transform derivatives back to physical element
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > for (unsigned int col = 0; col < num_derivatives; col++)
> > > > > {
> > > > > values[row] += transform[row][col]*derivatives[col];
> > > > > }
> > > > > }
> > > > > // Delete pointer to array of derivatives on FIAT element
> > > > > delete [] derivatives;
> > > > >
> > > > > // Delete pointer to array of combinations of derivatives and transform
> > > > > for (unsigned int row = 0; row < num_derivatives; row++)
> > > > > {
> > > > > delete [] combinations[row];
> > > > > delete [] transform[row];
> > > > > }
> > > > >
> > > > > delete [] combinations;
> > > > > delete [] transform;
> > > > > }
> > > > >
> > > > > /// Evaluate order n derivatives of all basis functions at given point in cell
> > > > > virtual void evaluate_basis_derivatives_all(unsigned int n,
> > > > > double* values,
> > > > > const double* coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
> > > > > }
> > > > >
> > > > > /// Evaluate linear functional for dof i on the function f
> > > > > virtual double evaluate_dof(unsigned int i,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // The reference points, direction and weights:
> > > > > static const double X[3][1][2] = {{{0, 0}}, {{1, 0}}, {{0, 1}}};
> > > > > static const double W[3][1] = {{1}, {1}, {1}};
> > > > > static const double D[3][1][1] = {{{1}}, {{1}}, {{1}}};
> > > > >
> > > > > const double * const * x = c.coordinates;
> > > > > double result = 0.0;
> > > > > // Iterate over the points:
> > > > > // Evaluate basis functions for affine mapping
> > > > > const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
> > > > > const double w1 = X[i][0][0];
> > > > > const double w2 = X[i][0][1];
> > > > >
> > > > > // Compute affine mapping y = F(X)
> > > > > double y[2];
> > > > > y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
> > > > > y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
> > > > >
> > > > > // Evaluate function at physical points
> > > > > double values[1];
> > > > > f.evaluate(values, y, c);
> > > > >
> > > > > // Map function values using appropriate mapping
> > > > > // Affine map: Do nothing
> > > > >
> > > > > // Note that we do not map the weights (yet).
> > > > >
> > > > > // Take directional components
> > > > > for(int k = 0; k < 1; k++)
> > > > > result += values[k]*D[i][0][k];
> > > > > // Multiply by weights
> > > > > result *= W[i][0];
> > > > >
> > > > > return result;
> > > > > }
> > > > >
> > > > > /// Evaluate linear functionals for all dofs on the function f
> > > > > virtual void evaluate_dofs(double* values,
> > > > > const ufc::function& f,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Interpolate vertex values from dof values
> > > > > virtual void interpolate_vertex_values(double* vertex_values,
> > > > > const double* dof_values,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > // Evaluate at vertices and use affine mapping
> > > > > vertex_values[0] = dof_values[0];
> > > > > vertex_values[1] = dof_values[1];
> > > > > vertex_values[2] = dof_values[2];
> > > > > }
> > > > >
> > > > > /// Return the number of sub elements (for a mixed element)
> > > > > virtual unsigned int num_sub_elements() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for sub element i (for a mixed element)
> > > > > virtual ufc::finite_element* create_sub_element(unsigned int i) const
> > > > > {
> > > > > return new poisson_auxiliary_1_finite_element_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for a local-to-global mapping of
> > > > > /// degrees of freedom (dofs).
> > > > >
> > > > >
> > > > > class poisson_auxiliary_1_dof_map_0: public ufc::dof_map
> > > > > {
> > > > > private:
> > > > >
> > > > > unsigned int __global_dimension;
> > > > >
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_auxiliary_1_dof_map_0() :ufc::dof_map()
> > > > > {
> > > > > __global_dimension = 0;
> > > > > }
> > > > > /// Destructor
> > > > > virtual ~poisson_auxiliary_1_dof_map_0()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the dof map
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "FFC dof map for FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1)";
> > > > > }
> > > > >
> > > > > /// Return true iff mesh entities of topological dimension d are needed
> > > > > virtual bool needs_mesh_entities(unsigned int d) const
> > > > > {
> > > > > switch ( d )
> > > > > {
> > > > > case 0:
> > > > > return true;
> > > > > break;
> > > > > case 1:
> > > > > return false;
> > > > > break;
> > > > > case 2:
> > > > > return false;
> > > > > break;
> > > > > }
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for mesh (return true iff init_cell() is needed)
> > > > > virtual bool init_mesh(const ufc::mesh& m)
> > > > > {
> > > > > __global_dimension = m.num_entities[0];
> > > > > return false;
> > > > > }
> > > > >
> > > > > /// Initialize dof map for given cell
> > > > > virtual void init_cell(const ufc::mesh& m,
> > > > > const ufc::cell& c)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Finish initialization of dof map for cells
> > > > > virtual void init_cell_finalize()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return the dimension of the global finite element function space
> > > > > virtual unsigned int global_dimension() const
> > > > > {
> > > > > return __global_dimension ;
> > > > > }
> > > > >
> > > > > /// Return the dimension of the local finite element function space for a cell
> > > > > virtual unsigned int local_dimension(const ufc::cell& c) const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > > /// Return the maximum dimension of the local finite element function space
> > > > > virtual unsigned int max_local_dimension() const
> > > > > {
> > > > > return 3;
> > > > > }
> > > > >
> > > > >
> > > > > // Return the geometric dimension of the coordinates this dof map provides
> > > > > virtual unsigned int geometric_dimension() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs on each cell facet
> > > > > virtual unsigned int num_facet_dofs() const
> > > > > {
> > > > > return 2;
> > > > > }
> > > > >
> > > > > /// Return the number of dofs associated with each cell entity of dimension d
> > > > > virtual unsigned int num_entity_dofs(unsigned int d) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-global mapping of dofs on a cell
> > > > > virtual void tabulate_dofs(unsigned int* dofs,
> > > > > const ufc::mesh& m,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > dofs[0] = c.entity_indices[0][0];
> > > > > dofs[1] = c.entity_indices[0][1];
> > > > > dofs[2] = c.entity_indices[0][2];
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping from facet dofs to cell dofs
> > > > > virtual void tabulate_facet_dofs(unsigned int* dofs,
> > > > > unsigned int facet) const
> > > > > {
> > > > > switch ( facet )
> > > > > {
> > > > > case 0:
> > > > > dofs[0] = 1;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 1:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 2;
> > > > > break;
> > > > > case 2:
> > > > > dofs[0] = 0;
> > > > > dofs[1] = 1;
> > > > > break;
> > > > > }
> > > > > }
> > > > >
> > > > > /// Tabulate the local-to-local mapping of dofs on entity (d, i)
> > > > > virtual void tabulate_entity_dofs(unsigned int* dofs,
> > > > > unsigned int d, unsigned int i) const
> > > > > {
> > > > > throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
> > > > > }
> > > > >
> > > > > /// Tabulate the coordinates of all dofs on a cell
> > > > > virtual void tabulate_coordinates(double** coordinates,
> > > > > const ufc::cell& c) const
> > > > > {
> > > > > const double * const * x = c.coordinates;
> > > > > coordinates[0][0] = x[0][0];
> > > > > coordinates[0][1] = x[0][1];
> > > > > coordinates[1][0] = x[1][0];
> > > > > coordinates[1][1] = x[1][1];
> > > > > coordinates[2][0] = x[2][0];
> > > > > coordinates[2][1] = x[2][1];
> > > > > }
> > > > >
> > > > > /// Return the number of sub dof maps (for a mixed element)
> > > > > virtual unsigned int num_sub_dof_maps() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Create a new dof_map for sub dof map i (for a mixed element)
> > > > > virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
> > > > > {
> > > > > return new poisson_auxiliary_1_dof_map_0();
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for the assembly of the global
> > > > > /// tensor corresponding to a form with r + n arguments, that is, a
> > > > > /// mapping
> > > > > ///
> > > > > /// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
> > > > > ///
> > > > > /// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
> > > > > /// global tensor A is defined by
> > > > > ///
> > > > > /// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
> > > > > ///
> > > > > /// where each argument Vj represents the application to the
> > > > > /// sequence of basis functions of Vj and w1, w2, ..., wn are given
> > > > > /// fixed functions (coefficients).
> > > > >
> > > > > class poisson_auxiliary_form_1: public ufc::form
> > > > > {
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > poisson_auxiliary_form_1() : ufc::form()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > virtual ~poisson_auxiliary_form_1()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the form
> > > > > virtual const char* signature() const
> > > > > {
> > > > > return "Auxiliary ufc::form to initialize standard functions, apply boundary conditions and obtain ufc::dof_map objects for continuous space(required for PUM objects) for a form containing discontinuous spaces.";
> > > > > }
> > > > >
> > > > > /// Return the rank of the global tensor (r)
> > > > > virtual unsigned int rank() const
> > > > > {
> > > > > return 1;
> > > > > }
> > > > >
> > > > > /// Return the number of coefficients (n)
> > > > > virtual unsigned int num_coefficients() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the number of cell integrals
> > > > > virtual unsigned int num_cell_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the number of exterior facet integrals
> > > > > virtual unsigned int num_exterior_facet_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the number of interior facet integrals
> > > > > virtual unsigned int num_interior_facet_integrals() const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new finite element for argument function i
> > > > > virtual ufc::finite_element* create_finite_element(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_auxiliary_1_finite_element_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_auxiliary_1_finite_element_0();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new dof map for argument function i
> > > > > virtual ufc::dof_map* create_dof_map(unsigned int i) const
> > > > > {
> > > > > switch ( i )
> > > > > {
> > > > > case 0:
> > > > > return new poisson_auxiliary_1_dof_map_0();
> > > > > break;
> > > > > case 1:
> > > > > return new poisson_auxiliary_1_dof_map_0();
> > > > > break;
> > > > > }
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new cell integral on sub domain i
> > > > > virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new exterior facet integral on sub domain i
> > > > > virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Create a new interior facet integral on sub domain i
> > > > > virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
> > > > > {
> > > > > return 0;
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > /// This class defines the interface for post-processing on vector x
> > > > > /// to obtain x0, u and j where,
> > > > > ///
> > > > > /// - x is the solution vector containing standard and enriched degrees of freedom
> > > > > /// defined on continuous/discontinuous space
> > > > > /// - u is the standard part of solution vector defined on continuous space
> > > > > /// - j is the enriched part pf solution vector defined on continuous space
> > > > > /// - x0 is the result vector, equall to u + j, defined on continuous space
> > > > > /// by considering enrichement function
> > > > > //
> > > > >
> > > > > // Dolfin includes
> > > > > #include <dolfin/common/NoDeleter.h>
> > > > > #include <dolfin/mesh/Mesh.h>
> > > > > #include <dolfin/fem/DofMap.h>
> > > > > #include <dolfin/la/GenericVector.h>
> > > > >
> > > > > // PartitionOfUnity includes
> > > > > #include <pum/PostProcess.h>
> > > > > #include <pum/FunctionSpace.h>
> > > > >
> > > > > namespace Poisson
> > > > > {
> > > > > class PostProcess: public pum::PostProcess
> > > > > {
> > > > > dolfin::Mesh& mesh;
> > > > > std::vector<const pum::GenericPUM*>& pums;
> > > > >
> > > > > public:
> > > > >
> > > > > /// Constructor
> > > > > PostProcess(dolfin::Mesh& mesh, std::vector<const pum::GenericPUM*>& pums): pum::PostProcess(mesh), mesh(mesh), pums(pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Destructor
> > > > > ~PostProcess()
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > /// Return a string identifying the underling element
> > > > > const char* signature() const
> > > > > {
> > > > > return "Interpolating results to the continuous space of MixedElement(*[FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None))], **{'value_shape': (2,) })";
> > > > > }
> > > > >
> > > > > /// Obtain result vector 'x0' from solution vector 'x'
> > > > > void interpolate(const dolfin::GenericVector& x, dolfin::GenericVector& x0) const
> > > > > {
> > > > >
> > > > > //poisson_1_dof_map_0_0 ufc_dof_map_0;
> > > > > //dolfin::DofMap dof_map_0(ufc_dof_map_0, mesh);
> > > > > //dolfin::DofMap dof_map_0(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_0_0()), dolfin::reference_to_no_delete_pointer(mesh));
> > > > > dolfin::DofMap dof_map_0(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_0_0()), mesh);
> > > > > unsigned int num_standard_dofs_0 = dof_map_0.global_dimension();
> > > > >
> > > > > double value, h;
> > > > >
> > > > > /// selecting standard degrees of freedom related to field 0 from the solution vector
> > > > >
> > > > > double* values_0 = new double[num_standard_dofs_0];
> > > > > unsigned int* positions_0 = new unsigned int [num_standard_dofs_0];
> > > > >
> > > > > for (unsigned int i = 0; i < num_standard_dofs_0; ++i)
> > > > > positions_0[i] = i;
> > > > >
> > > > > x.get(values_0, num_standard_dofs_0, positions_0);
> > > > > x0.set(values_0, num_standard_dofs_0, positions_0);
> > > > >
> > > > >
> > > > >
> > > > > /// selecting enriched degrees of freedom related to field 0 from the solution vector
> > > > > std::vector <std::vector<unsigned int> > enhanced_dof_maps_0;
> > > > > enhanced_dof_maps_0.resize(num_standard_dofs_0);
> > > > >
> > > > > std::vector<unsigned int> enhanced_dof_values_0;
> > > > > enhanced_dof_values_0.resize(num_standard_dofs_0);
> > > > >
> > > > > compute_enhanced_dof_maps(*pums[0], dof_map_0, enhanced_dof_maps_0);
> > > > > compute_enhanced_dof_values(*pums[0], dof_map_0, enhanced_dof_values_0);
> > > > >
> > > > >
> > > > > for (unsigned int i = 0; i != num_standard_dofs_0; ++i)
> > > > > {
> > > > > unsigned int pos = i;
> > > > >
> > > > > for (std::vector<unsigned int>::const_iterator it = enhanced_dof_maps_0[i].begin();
> > > > > it != enhanced_dof_maps_0[i].end(); ++it)
> > > > > {
> > > > > //h = pums[0]->enhanced_node_value(*it);
> > > > > h = enhanced_dof_values_0[i];
> > > > > unsigned int pos_n = *it + num_standard_dofs_0;
> > > > >
> > > > > x.get(&value, 1, &pos_n);
> > > > > value *= h;
> > > > > x0.add(&value, 1, &pos);
> > > > > }
> > > > > }
> > > > >
> > > > >
> > > > > // memory clean up
> > > > >
> > > > > delete[] values_0;
> > > > > delete[] positions_0;
> > > > >
> > > > > x0.apply();
> > > > > }
> > > > >
> > > > > /// Obtain continuous u and discontinuous j parts of solution vector 'x'
> > > > > void interpolate(const dolfin::GenericVector& x, dolfin::GenericVector& u, dolfin::GenericVector& j) const
> > > > > {
> > > > >
> > > > > //poisson_1_dof_map_0_0 ufc_dof_map_0;
> > > > > //dolfin::DofMap dof_map_0(ufc_dof_map_0, mesh);
> > > > > //dolfin::DofMap dof_map_0(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_0_0()), dolfin::reference_to_no_delete_pointer(mesh));
> > > > > dolfin::DofMap dof_map_0(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_0_0()), mesh);
> > > > > unsigned int num_standard_dofs_0 = dof_map_0.global_dimension();
> > > > >
> > > > > double value;
> > > > >
> > > > > /// selecting standard degrees of freedom related to field 0 from the solution vector
> > > > > double* values_0 = new double[num_standard_dofs_0];
> > > > > unsigned int* positions_0 = new unsigned int [num_standard_dofs_0];
> > > > >
> > > > > for (unsigned int i = 0; i < num_standard_dofs_0; ++i)
> > > > > positions_0[i] = i;
> > > > >
> > > > > x.get(values_0, num_standard_dofs_0, positions_0);
> > > > > u.set(values_0, num_standard_dofs_0, positions_0);
> > > > >
> > > > >
> > > > >
> > > > > /// selecting enriched degrees of freedom related to field 0 from the solution vector
> > > > > std::vector <std::vector<unsigned int> > enhanced_dof_maps_0;
> > > > > enhanced_dof_maps_0.resize(num_standard_dofs_0);
> > > > >
> > > > > compute_enhanced_dof_maps(*pums[0], dof_map_0, enhanced_dof_maps_0);
> > > > >
> > > > > for (unsigned int i = 0; i != num_standard_dofs_0; ++i)
> > > > > {
> > > > > unsigned int pos = i ;
> > > > >
> > > > > for (std::vector<unsigned int>::const_iterator it = enhanced_dof_maps_0[i].begin();
> > > > > it != enhanced_dof_maps_0[i].end(); ++it)
> > > > > {
> > > > > unsigned int pos_n = *it + num_standard_dofs_0;
> > > > >
> > > > > x.get(&value, 1, &pos_n);
> > > > > j.set(&value, 1, &pos);
> > > > > }
> > > > > }
> > > > >
> > > > >
> > > > > // memory clean up
> > > > >
> > > > > delete[] values_0;
> > > > > delete[] positions_0;
> > > > >
> > > > > u.apply();
> > > > > j.apply();
> > > > > }
> > > > >
> > > > > };
> > > > > }
> > > > >
> > > > > // DOLFIN wrappers
> > > > >
> > > > > // Standard library includes
> > > > > #include <string>
> > > > >
> > > > > // DOLFIN includes
> > > > > #include <dolfin/common/NoDeleter.h>
> > > > > #include <dolfin/fem/FiniteElement.h>
> > > > > #include <dolfin/fem/DofMap.h>
> > > > > #include <dolfin/fem/Form.h>
> > > > > #include <dolfin/function/FunctionSpace.h>
> > > > > #include <dolfin/function/Function.h>
> > > > > #include <dolfin/function/GenericFunction.h>
> > > > > #include <dolfin/function/CoefficientAssigner.h>
> > > > >
> > > > > namespace Poisson
> > > > > {
> > > > >
> > > > > class CoefficientSpace_f: public dolfin::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > CoefficientSpace_f(const dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_1()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_1_dof_map_1()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_f(dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_1()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_1()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_f(boost::shared_ptr<dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_1()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_1()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_f(boost::shared_ptr<const dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_1()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_1()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~CoefficientSpace_f()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > class CoefficientSpace_g: public dolfin::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > CoefficientSpace_g(const dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_2()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_1_dof_map_2()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_g(dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_2()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_2()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_g(boost::shared_ptr<dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_2()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_2()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_g(boost::shared_ptr<const dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_2()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_2()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~CoefficientSpace_g()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > class CoefficientSpace_k: public dolfin::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > CoefficientSpace_k(const dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_2()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_0_dof_map_2()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_k(dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_2()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_2()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_k(boost::shared_ptr<dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_2()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_2()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_k(boost::shared_ptr<const dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_2()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_2()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~CoefficientSpace_k()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > class CoefficientSpace_w: public dolfin::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > CoefficientSpace_w(const dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_3()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_0_dof_map_3()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_w(dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_3()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_3()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_w(boost::shared_ptr<dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_3()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_3()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > CoefficientSpace_w(boost::shared_ptr<const dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_3()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_3()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~CoefficientSpace_w()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > class Form_0_FunctionSpace_0: public pum::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > Form_0_FunctionSpace_0(const dolfin::Mesh & mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_0_dof_map_0(pums)), mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_0_FunctionSpace_0(dolfin::Mesh & mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_0(pums)), mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_0_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_0(pums)), *mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_0_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_0(pums)), *mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~Form_0_FunctionSpace_0()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > class Form_0_FunctionSpace_1: public pum::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > Form_0_FunctionSpace_1(const dolfin::Mesh & mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_1()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_0_dof_map_1(pums)), mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_0_FunctionSpace_1(dolfin::Mesh & mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_1()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_1(pums)), mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_0_FunctionSpace_1(boost::shared_ptr<dolfin::Mesh> mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_1()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_1(pums)), *mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_0_FunctionSpace_1(boost::shared_ptr<const dolfin::Mesh> mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_0_finite_element_1()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_0_dof_map_1(pums)), *mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~Form_0_FunctionSpace_1()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > typedef CoefficientSpace_k Form_0_FunctionSpace_2;
> > > > >
> > > > > typedef CoefficientSpace_w Form_0_FunctionSpace_3;
> > > > >
> > > > > class Form_0: public dolfin::Form
> > > > > {
> > > > > public:
> > > > >
> > > > > // Constructor
> > > > > Form_0(const pum::FunctionSpace& V0, const pum::FunctionSpace& V1):
> > > > > dolfin::Form(2, 2), k(*this, 0), w(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = reference_to_no_delete_pointer(V0);
> > > > > _function_spaces[1] = reference_to_no_delete_pointer(V1);
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_0(V0.pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_0(const pum::FunctionSpace& V0, const pum::FunctionSpace& V1, dolfin::GenericFunction & k, dolfin::GenericFunction & w):
> > > > > dolfin::Form(2, 2), k(*this, 0), w(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = reference_to_no_delete_pointer(V0);
> > > > > _function_spaces[1] = reference_to_no_delete_pointer(V1);
> > > > >
> > > > > this->k = k;
> > > > > this->w = w;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_0(V0.pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_0(const pum::FunctionSpace& V0, const pum::FunctionSpace& V1, boost::shared_ptr<dolfin::GenericFunction> k, boost::shared_ptr<dolfin::GenericFunction> w):
> > > > > dolfin::Form(2, 2), k(*this, 0), w(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = reference_to_no_delete_pointer(V0);
> > > > > _function_spaces[1] = reference_to_no_delete_pointer(V1);
> > > > >
> > > > > this->k = *k;
> > > > > this->w = *w;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_0(V0.pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_0(boost::shared_ptr<const pum::FunctionSpace> V0, boost::shared_ptr<const pum::FunctionSpace> V1):
> > > > > dolfin::Form(2, 2), k(*this, 0), w(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = V0;
> > > > > _function_spaces[1] = V1;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_0(V0->pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_0(boost::shared_ptr<const pum::FunctionSpace> V0, boost::shared_ptr<const pum::FunctionSpace> V1, dolfin::GenericFunction & k, dolfin::GenericFunction & w):
> > > > > dolfin::Form(2, 2), k(*this, 0), w(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = V0;
> > > > > _function_spaces[1] = V1;
> > > > >
> > > > > this->k = k;
> > > > > this->w = w;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_0(V0->pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_0(boost::shared_ptr<const pum::FunctionSpace> V0, boost::shared_ptr<const pum::FunctionSpace> V1, boost::shared_ptr<dolfin::GenericFunction> k, boost::shared_ptr<dolfin::GenericFunction> w):
> > > > > dolfin::Form(2, 2), k(*this, 0), w(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = V0;
> > > > > _function_spaces[1] = V1;
> > > > >
> > > > > this->k = *k;
> > > > > this->w = *w;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_0(V0->pums));
> > > > > }
> > > > >
> > > > > // Destructor
> > > > > ~Form_0()
> > > > > {}
> > > > >
> > > > > /// Return the number of the coefficient with this name
> > > > > virtual dolfin::uint coefficient_number(const std::string& name) const
> > > > > {
> > > > > if(name == "k") return 0;
> > > > > else if(name == "w") return 1;
> > > > > dolfin::error("Invalid coefficient.");
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the name of the coefficient with this number
> > > > > virtual std::string coefficient_name(dolfin::uint i) const
> > > > > {
> > > > > switch(i)
> > > > > {
> > > > > case 0: return "k";
> > > > > case 1: return "w";
> > > > > }
> > > > > dolfin::error("Invalid coefficient.");
> > > > > return "unnamed";
> > > > > }
> > > > >
> > > > > // Typedefs
> > > > > typedef Form_0_FunctionSpace_0 TestSpace;
> > > > > typedef Form_0_FunctionSpace_1 TrialSpace;
> > > > > typedef Form_0_FunctionSpace_2 CoefficientSpace_k;
> > > > > typedef Form_0_FunctionSpace_3 CoefficientSpace_w;
> > > > >
> > > > > // Coefficients
> > > > > dolfin::CoefficientAssigner k;
> > > > > dolfin::CoefficientAssigner w;
> > > > > };
> > > > >
> > > > > class Form_1_FunctionSpace_0: public pum::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > Form_1_FunctionSpace_0(const dolfin::Mesh & mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_1_dof_map_0(pums)), mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_1_FunctionSpace_0(dolfin::Mesh & mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_0(pums)), mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_1_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_0(pums)), *mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_1_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh ,const std::vector<const pum::GenericPUM*>& pums):
> > > > > pum::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_1_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_1_dof_map_0(pums)), *mesh)) ,pums)
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~Form_1_FunctionSpace_0()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > typedef CoefficientSpace_f Form_1_FunctionSpace_1;
> > > > >
> > > > > typedef CoefficientSpace_g Form_1_FunctionSpace_2;
> > > > >
> > > > > class Form_1: public dolfin::Form
> > > > > {
> > > > > public:
> > > > >
> > > > > // Constructor
> > > > > Form_1(const pum::FunctionSpace& V0):
> > > > > dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = reference_to_no_delete_pointer(V0);
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_1(V0.pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_1(const pum::FunctionSpace& V0, dolfin::GenericFunction & f, dolfin::GenericFunction & g):
> > > > > dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = reference_to_no_delete_pointer(V0);
> > > > >
> > > > > this->f = f;
> > > > > this->g = g;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_1(V0.pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_1(const pum::FunctionSpace& V0, boost::shared_ptr<dolfin::GenericFunction> f, boost::shared_ptr<dolfin::GenericFunction> g):
> > > > > dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = reference_to_no_delete_pointer(V0);
> > > > >
> > > > > this->f = *f;
> > > > > this->g = *g;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_1(V0.pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_1(boost::shared_ptr<const pum::FunctionSpace> V0):
> > > > > dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = V0;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_1(V0->pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_1(boost::shared_ptr<const pum::FunctionSpace> V0, dolfin::GenericFunction & f, dolfin::GenericFunction & g):
> > > > > dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = V0;
> > > > >
> > > > > this->f = f;
> > > > > this->g = g;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_1(V0->pums));
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_1(boost::shared_ptr<const pum::FunctionSpace> V0, boost::shared_ptr<dolfin::GenericFunction> f, boost::shared_ptr<dolfin::GenericFunction> g):
> > > > > dolfin::Form(1, 2), f(*this, 0), g(*this, 1)
> > > > > {
> > > > > _function_spaces[0] = V0;
> > > > >
> > > > > this->f = *f;
> > > > > this->g = *g;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_form_1(V0->pums));
> > > > > }
> > > > >
> > > > > // Destructor
> > > > > ~Form_1()
> > > > > {}
> > > > >
> > > > > /// Return the number of the coefficient with this name
> > > > > virtual dolfin::uint coefficient_number(const std::string& name) const
> > > > > {
> > > > > if(name == "f") return 0;
> > > > > else if(name == "g") return 1;
> > > > > dolfin::error("Invalid coefficient.");
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the name of the coefficient with this number
> > > > > virtual std::string coefficient_name(dolfin::uint i) const
> > > > > {
> > > > > switch(i)
> > > > > {
> > > > > case 0: return "f";
> > > > > case 1: return "g";
> > > > > }
> > > > > dolfin::error("Invalid coefficient.");
> > > > > return "unnamed";
> > > > > }
> > > > >
> > > > > // Typedefs
> > > > > typedef Form_1_FunctionSpace_0 TestSpace;
> > > > > typedef Form_1_FunctionSpace_1 CoefficientSpace_f;
> > > > > typedef Form_1_FunctionSpace_2 CoefficientSpace_g;
> > > > >
> > > > > // Coefficients
> > > > > dolfin::CoefficientAssigner f;
> > > > > dolfin::CoefficientAssigner g;
> > > > > };
> > > > >
> > > > > // Class typedefs
> > > > > typedef Form_0 BilinearForm;
> > > > > typedef Form_1 LinearForm;
> > > > > typedef Form_0::TestSpace FunctionSpace;
> > > > >
> > > > > } // namespace Poisson
> > > > >
> > > > > // DOLFIN wrappers
> > > > >
> > > > > // Standard library includes
> > > > > #include <string>
> > > > >
> > > > > // DOLFIN includes
> > > > > #include <dolfin/common/NoDeleter.h>
> > > > > #include <dolfin/fem/FiniteElement.h>
> > > > > #include <dolfin/fem/DofMap.h>
> > > > > #include <dolfin/fem/Form.h>
> > > > > #include <dolfin/function/FunctionSpace.h>
> > > > > #include <dolfin/function/Function.h>
> > > > > #include <dolfin/function/GenericFunction.h>
> > > > > #include <dolfin/function/CoefficientAssigner.h>
> > > > >
> > > > > namespace Poisson
> > > > > {
> > > > >
> > > > > class Form_auxiliary_0_FunctionSpace_auxiliary_0: public dolfin::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > Form_auxiliary_0_FunctionSpace_auxiliary_0(const dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_auxiliary_0_dof_map_0()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_0_FunctionSpace_auxiliary_0(dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_0_dof_map_0()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_0_FunctionSpace_auxiliary_0(boost::shared_ptr<dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_0_dof_map_0()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_0_FunctionSpace_auxiliary_0(boost::shared_ptr<const dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_0_dof_map_0()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~Form_auxiliary_0_FunctionSpace_auxiliary_0()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > class Form_auxiliary_0_FunctionSpace_auxiliary_1: public dolfin::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > Form_auxiliary_0_FunctionSpace_auxiliary_1(const dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_auxiliary_0_dof_map_0()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_0_FunctionSpace_auxiliary_1(dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_0_dof_map_0()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_0_FunctionSpace_auxiliary_1(boost::shared_ptr<dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_0_dof_map_0()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_0_FunctionSpace_auxiliary_1(boost::shared_ptr<const dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_0_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_0_dof_map_0()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~Form_auxiliary_0_FunctionSpace_auxiliary_1()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > class Form_auxiliary_0: public dolfin::Form
> > > > > {
> > > > > public:
> > > > >
> > > > > // Constructor
> > > > > Form_auxiliary_0(const dolfin::FunctionSpace& V0, const dolfin::FunctionSpace& V1):
> > > > > dolfin::Form(2, 0)
> > > > > {
> > > > > _function_spaces[0] = reference_to_no_delete_pointer(V0);
> > > > > _function_spaces[1] = reference_to_no_delete_pointer(V1);
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_auxiliary_form_0());
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_auxiliary_0(boost::shared_ptr<const dolfin::FunctionSpace> V0, boost::shared_ptr<const dolfin::FunctionSpace> V1):
> > > > > dolfin::Form(2, 0)
> > > > > {
> > > > > _function_spaces[0] = V0;
> > > > > _function_spaces[1] = V1;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_auxiliary_form_0());
> > > > > }
> > > > >
> > > > > // Destructor
> > > > > ~Form_auxiliary_0()
> > > > > {}
> > > > >
> > > > > /// Return the number of the coefficient with this name
> > > > > virtual dolfin::uint coefficient_number(const std::string& name) const
> > > > > {
> > > > > dolfin::error("No coefficients.");
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the name of the coefficient with this number
> > > > > virtual std::string coefficient_name(dolfin::uint i) const
> > > > > {
> > > > > dolfin::error("No coefficients.");
> > > > > return "unnamed";
> > > > > }
> > > > >
> > > > > // Typedefs
> > > > > typedef Form_auxiliary_0_FunctionSpace_auxiliary_0 TestSpace;
> > > > > typedef Form_auxiliary_0_FunctionSpace_auxiliary_1 TrialSpace;
> > > > >
> > > > > // Coefficients
> > > > > };
> > > > >
> > > > > class Form_auxiliary_1_FunctionSpace_auxiliary_0: public dolfin::FunctionSpace
> > > > > {
> > > > > public:
> > > > >
> > > > >
> > > > > Form_auxiliary_1_FunctionSpace_auxiliary_0(const dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement
> > > > > (boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_1_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>
> > > > > (new poisson_auxiliary_1_dof_map_0()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_1_FunctionSpace_auxiliary_0(dolfin::Mesh & mesh):
> > > > > dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_1_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_1_dof_map_0()), mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_1_FunctionSpace_auxiliary_0(boost::shared_ptr<dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_1_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_1_dof_map_0()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > > Form_auxiliary_1_FunctionSpace_auxiliary_0(boost::shared_ptr<const dolfin::Mesh> mesh):
> > > > > dolfin::FunctionSpace(mesh,
> > > > > boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson_auxiliary_1_finite_element_0()))),
> > > > > boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dof_map>(new poisson_auxiliary_1_dof_map_0()), *mesh)))
> > > > > {
> > > > > // Do nothing
> > > > > }
> > > > >
> > > > >
> > > > > ~Form_auxiliary_1_FunctionSpace_auxiliary_0()
> > > > > {
> > > > > }
> > > > >
> > > > > };
> > > > >
> > > > > class Form_auxiliary_1: public dolfin::Form
> > > > > {
> > > > > public:
> > > > >
> > > > > // Constructor
> > > > > Form_auxiliary_1(const dolfin::FunctionSpace& V0):
> > > > > dolfin::Form(1, 0)
> > > > > {
> > > > > _function_spaces[0] = reference_to_no_delete_pointer(V0);
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_auxiliary_form_0());
> > > > > }
> > > > >
> > > > > // Constructor
> > > > > Form_auxiliary_1(boost::shared_ptr<const dolfin::FunctionSpace> V0):
> > > > > dolfin::Form(1, 0)
> > > > > {
> > > > > _function_spaces[0] = V0;
> > > > >
> > > > > _ufc_form = boost::shared_ptr<const ufc::form>(new poisson_auxiliary_form_0());
> > > > > }
> > > > >
> > > > > // Destructor
> > > > > ~Form_auxiliary_1()
> > > > > {}
> > > > >
> > > > > /// Return the number of the coefficient with this name
> > > > > virtual dolfin::uint coefficient_number(const std::string& name) const
> > > > > {
> > > > > dolfin::error("No coefficients.");
> > > > > return 0;
> > > > > }
> > > > >
> > > > > /// Return the name of the coefficient with this number
> > > > > virtual std::string coefficient_name(dolfin::uint i) const
> > > > > {
> > > > > dolfin::error("No coefficients.");
> > > > > return "unnamed";
> > > > > }
> > > > >
> > > > > // Typedefs
> > > > > typedef Form_auxiliary_1_FunctionSpace_auxiliary_0 TestSpace;
> > > > >
> > > > > // Coefficients
> > > > > };
> > > > >
> > > > > // Class typedefs
> > > > > typedef Form_auxiliary_0 BilinearForm_auxiliary;
> > > > > typedef Form_auxiliary_1 LinearForm_auxiliary;
> > > > > typedef Form_auxiliary_0::TestSpace FunctionSpace_auxiliary;
> > > > >
> > > > > } // namespace Poisson
> > > > >
> > > > > #endif
> > > >
> > > > > # Copyright (C) 2008-2009 Mehdi Nikbakht and Garth N. Wells.
> > > > > # Licensed under the GNU GPL Version 3.0 or any later version.
> > > > > #
> > > > > # The bilinear form a(v, u) and linear form L(v) for
> > > > > # Poisson's equation with discontinuities.
> > > > > #
> > > > > # Compile this form with FFC: ffc-pum -l dolfin Poisson.ufl
> > > > > #
> > > > >
> > > > > elem_cont = FiniteElement("CG", triangle, 1)
> > > > > elem_discont = ElementRestriction(elem_cont, dc) # or ec[dc]
> > > > >
> > > > > element = elem_cont + elem_discont
> > > > >
> > > > > (vc, vd) = TestFunctions(element)
> > > > > (uc, ud) = TrialFunctions(element)
> > > > >
> > > > > v = vc + vd
> > > > > u = uc + ud
> > > > >
> > > > >
> > > > > k = Constant(triangle)
> > > > > f = Coefficient(elem_cont)
> > > > > w = Coefficient(elem_cont)
> > > > > g = Coefficient(elem_cont)
> > > > >
> > > > > a = w*dot(grad(v), grad(u))*dx + k*inner(vd, ud)*dc #+ (u*v)('-')*dS
> > > > > L = v*f*dx - v*g*ds
> > > > >
> > > >
> > >
>
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