Mehdi
>
> > Please have a look on the tabulate_Tensor function inside generated code
> > for Poisson demo in the attached files.
>
> It looks too complex for me. What I propose is a very simple extension
> of UFC (a function that is simpler than what we have now) which would
> allow users (such as myself) to handle the complexity elsewhere.
>
> --
> Anders
>
>
> > // This code conforms with the UFC specification version 1.4
> > // and was automatically generated by FFC version 0.9.2+.
> > //
> > // This code was generated with the option '-l dolfin' and
> > // contains DOLFIN-specific wrappers that depend on DOLFIN.
> > //
> > // This code was generated with the following parameters:
> > //
> > // cache_dir: ''
> > // convert_exceptions_to_warnings: False
> > // cpp_optimize: False
> > // epsilon: 1e-14
> > // form_postfix: True
> > // format: 'dolfin'
> > // log_level: 20
> > // log_prefix: ''
> > // optimize: False
> > // output_dir: '.'
> > // precision: 15
> > // quadrature_degree: 'auto'
> > // quadrature_rule: 'auto'
> > // representation: 'quadrature'
> > // split: False
> >
> > #ifndef __POISSON_H
> > #define __POISSON_H
> >
> > #include <cmath>
> > #include <algorithm>
> > #include <stdexcept>
> > #include <fstream>
> > #include <boost/assign/list_of.hpp>
> > #include <ufc.h>
> > #include <pum/GenericPUM.h>
> >
> > /// This class defines the interface for a finite element.
> >
> > class poisson_finite_element_0: public ufc::finite_element
> > {
> > public:
> >
> > /// Constructor
> > poisson_finite_element_0() : ufc::finite_element()
> > {
> > // Do nothing
> > }
> >
> > /// Destructor
> > virtual ~poisson_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 * 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
> >
> > // Compute constants
> > const double C0 = x[1][0] + x[2][0];
> > const double C1 = x[1][1] + x[2][1];
> >
> > // Get coordinates and map to the reference (FIAT) element
> > double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
> > double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
> >
> > // Reset values.
> > *values = 0.000000000000000;
> >
> > // Map degree of freedom to element degree of freedom
> > const unsigned int dof = i;
> >
> > // Array of basisvalues.
> > double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
> >
> > // Declare helper variables.
> > unsigned int rr = 0;
> > unsigned int ss = 0;
> > double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
> >
> > // Compute basisvalues.
> > basisvalues[0] = 1.000000000000000;
> > basisvalues[1] = tmp0;
> > for (unsigned int r = 0; r < 1; r++)
> > {
> > rr = (r + 1)*(r + 1 + 1)/2 + 1;
> > ss = r*(r + 1)/2;
> > basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
> > }// end loop over 'r'
> > for (unsigned int r = 0; r < 2; r++)
> > {
> > for (unsigned int s = 0; s < 2 - r; s++)
> > {
> > rr = (r + s)*(r + s + 1)/2 + s;
> > basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Table(s) of coefficients.
> > static const double coefficients0[3][3] = \
> > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.000000000000000, 0.333333333333333}};
> >
> > // Compute value(s).
> > for (unsigned int r = 0; r < 3; r++)
> > {
> > *values += coefficients0[dof][r]*basisvalues[r];
> > }// end loop over 'r'
> > }
> >
> > /// Evaluate all basis functions at given point in cell
> > virtual void evaluate_basis_all(double* values,
> > const double* coordinates,
> > const ufc::cell& c) const
> > {
> > // Helper variable to hold values of a single dof.
> > double dof_values = 0.000000000000000;
> >
> > // Loop dofs and call evaluate_basis.
> > for (unsigned int r = 0; r < 3; r++)
> > {
> > evaluate_basis(r, &dof_values, coordinates, c);
> > values[r] = dof_values;
> > }// end loop over 'r'
> > }
> >
> > /// 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 * 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 K_00 = J_11 / detJ;
> > const double K_01 = -J_01 / detJ;
> > const double K_10 = -J_10 / detJ;
> > const double K_11 = J_00 / detJ;
> >
> > // Compute constants
> > const double C0 = x[1][0] + x[2][0];
> > const double C1 = x[1][1] + x[2][1];
> >
> > // Get coordinates and map to the reference (FIAT) element
> > double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
> > double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
> >
> > // Compute number of derivatives.
> > unsigned int num_derivatives = 1;
> > for (unsigned int r = 0; r < n; r++)
> > {
> > num_derivatives *= 2;
> > }// end loop over 'r'
> >
> > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > unsigned int **combinations = new unsigned int *[num_derivatives];
> > for (unsigned int row = 0; row < num_derivatives; row++)
> > {
> > combinations[row] = new unsigned int [n];
> > for (unsigned int col = 0; col < n; col++)
> > combinations[row][col] = 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] = {{K_00, K_01}, {K_10, K_11}};
> >
> > // 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. Assuming that values is always an array.
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > values[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Map degree of freedom to element degree of freedom
> > const unsigned int dof = i;
> >
> > // Array of basisvalues.
> > double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
> >
> > // Declare helper variables.
> > unsigned int rr = 0;
> > unsigned int ss = 0;
> > double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
> >
> > // Compute basisvalues.
> > basisvalues[0] = 1.000000000000000;
> > basisvalues[1] = tmp0;
> > for (unsigned int r = 0; r < 1; r++)
> > {
> > rr = (r + 1)*(r + 1 + 1)/2 + 1;
> > ss = r*(r + 1)/2;
> > basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
> > }// end loop over 'r'
> > for (unsigned int r = 0; r < 2; r++)
> > {
> > for (unsigned int s = 0; s < 2 - r; s++)
> > {
> > rr = (r + s)*(r + s + 1)/2 + s;
> > basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Table(s) of coefficients.
> > static const double coefficients0[3][3] = \
> > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.000000000000000, 0.333333333333333}};
> >
> > // Tables of derivatives of the polynomial base (transpose).
> > static const double dmats0[3][3] = \
> > {{0.000000000000000, 0.000000000000000, 0.000000000000000},
> > {4.898979485566356, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 0.000000000000000}};
> >
> > static const double dmats1[3][3] = \
> > {{0.000000000000000, 0.000000000000000, 0.000000000000000},
> > {2.449489742783178, 0.000000000000000, 0.000000000000000},
> > {4.242640687119285, 0.000000000000000, 0.000000000000000}};
> >
> > // Compute reference derivatives.
> > // Declare pointer to array of derivatives on FIAT element.
> > double *derivatives = new double[num_derivatives];
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > derivatives[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Declare derivative matrix (of polynomial basis).
> > double dmats[3][3] = \
> > {{1.000000000000000, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 1.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 1.000000000000000}};
> >
> > // Declare (auxiliary) derivative matrix (of polynomial basis).
> > double dmats_old[3][3] = \
> > {{1.000000000000000, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 1.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 1.000000000000000}};
> >
> > // Loop possible derivatives.
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > // Resetting dmats values to compute next derivative.
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > dmats[t][u] = 0.000000000000000;
> > if (t == u)
> > {
> > dmats[t][u] = 1.000000000000000;
> > }
> >
> > }// end loop over 'u'
> > }// end loop over 't'
> >
> > // Looping derivative order to generate dmats.
> > for (unsigned int s = 0; s < n; s++)
> > {
> > // Updating dmats_old with new values and resetting dmats.
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > dmats_old[t][u] = dmats[t][u];
> > dmats[t][u] = 0.000000000000000;
> > }// end loop over 'u'
> > }// end loop over 't'
> >
> > // Update dmats using an inner product.
> > if (combinations[r][s] == 0)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > for (unsigned int tu = 0; tu < 3; tu++)
> > {
> > dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
> > }// end loop over 'tu'
> > }// end loop over 'u'
> > }// end loop over 't'
> > }
> >
> > if (combinations[r][s] == 1)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > for (unsigned int tu = 0; tu < 3; tu++)
> > {
> > dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
> > }// end loop over 'tu'
> > }// end loop over 'u'
> > }// end loop over 't'
> > }
> >
> > }// end loop over 's'
> > for (unsigned int s = 0; s < 3; s++)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
> > }// end loop over 't'
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Transform derivatives back to physical element
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > for (unsigned int s = 0; s < num_derivatives; s++)
> > {
> > values[r] += transform[r][s]*derivatives[s];
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Delete pointer to array of derivatives on FIAT element
> > delete [] derivatives;
> >
> > // Delete pointer to array of combinations of derivatives and transform
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > delete [] combinations[r];
> > }// end loop over 'r'
> > delete [] combinations;
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > delete [] transform[r];
> > }// end loop over 'r'
> > 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
> > {
> > // Compute number of derivatives.
> > unsigned int num_derivatives = 1;
> > for (unsigned int r = 0; r < n; r++)
> > {
> > num_derivatives *= 2;
> > }// end loop over 'r'
> >
> > // Helper variable to hold values of a single dof.
> > double *dof_values = new double[num_derivatives];
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > dof_values[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Loop dofs and call evaluate_basis_derivatives.
> > for (unsigned int r = 0; r < 3; r++)
> > {
> > evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
> > for (unsigned int s = 0; s < num_derivatives; s++)
> > {
> > values[r*num_derivatives + s] = dof_values[s];
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Delete pointer.
> > delete [] dof_values;
> > }
> >
> > /// 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
> > {
> > // Declare variables for result of evaluation.
> > double vals[1];
> >
> > // Declare variable for physical coordinates.
> > double y[2];
> > const double * const * x = c.coordinates;
> > switch (i)
> > {
> > case 0:
> > {
> > y[0] = x[0][0];
> > y[1] = x[0][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > case 1:
> > {
> > y[0] = x[1][0];
> > y[1] = x[1][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > case 2:
> > {
> > y[0] = x[2][0];
> > y[1] = x[2][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > }
> >
> > return 0.000000000000000;
> > }
> >
> > /// 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
> > {
> > // Declare variables for result of evaluation.
> > double vals[1];
> >
> > // Declare variable for physical coordinates.
> > double y[2];
> > const double * const * x = c.coordinates;
> > y[0] = x[0][0];
> > y[1] = x[0][1];
> > f.evaluate(vals, y, c);
> > values[0] = vals[0];
> > y[0] = x[1][0];
> > y[1] = x[1][1];
> > f.evaluate(vals, y, c);
> > values[1] = vals[0];
> > y[0] = x[2][0];
> > y[1] = x[2][1];
> > f.evaluate(vals, y, c);
> > values[2] = vals[0];
> > }
> >
> > /// Interpolate vertex values from dof values
> > virtual void interpolate_vertex_values(double* vertex_values,
> > const double* dof_values,
> > const ufc::cell& c) const
> > {
> > // Evaluate function and change variables
> > 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 0;
> > }
> >
> > /// 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 0;
> > }
> >
> > };
> >
> > /// This class defines the interface for a finite element.
> >
> > class poisson_finite_element_1: public ufc::finite_element
> > {
> > public:
> >
> > /// Constructor
> > poisson_finite_element_1() : ufc::finite_element()
> > {
> > // Do nothing
> > }
> >
> > /// Destructor
> > virtual ~poisson_finite_element_1()
> > {
> > // Do nothing
> > }
> >
> > /// Return a string identifying the finite element
> > virtual const char* signature() const
> > {
> > return "EnrichedElement(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None)))";
> > }
> >
> > /// 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 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 * 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
> >
> > // Compute constants
> > const double C0 = x[1][0] + x[2][0];
> > const double C1 = x[1][1] + x[2][1];
> >
> > // Get coordinates and map to the reference (FIAT) element
> > double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
> > double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
> >
> > // Reset values.
> > values[0] = 0.000000000000000;
> > values[1] = 0.000000000000000;
> > if (0 <= i && i <= 2)
> > {
> > // Map degree of freedom to element degree of freedom
> > const unsigned int dof = i;
> >
> > // Array of basisvalues.
> > double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
> >
> > // Declare helper variables.
> > unsigned int rr = 0;
> > unsigned int ss = 0;
> > double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
> >
> > // Compute basisvalues.
> > basisvalues[0] = 1.000000000000000;
> > basisvalues[1] = tmp0;
> > for (unsigned int r = 0; r < 1; r++)
> > {
> > rr = (r + 1)*(r + 1 + 1)/2 + 1;
> > ss = r*(r + 1)/2;
> > basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
> > }// end loop over 'r'
> > for (unsigned int r = 0; r < 2; r++)
> > {
> > for (unsigned int s = 0; s < 2 - r; s++)
> > {
> > rr = (r + s)*(r + s + 1)/2 + s;
> > basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Table(s) of coefficients.
> > static const double coefficients0[3][3] = \
> > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.000000000000000, 0.333333333333333}};
> >
> > // Compute value(s).
> > for (unsigned int r = 0; r < 3; r++)
> > {
> > values[0] += coefficients0[dof][r]*basisvalues[r];
> > }// end loop over 'r'
> > }
> >
> > if (3 <= i && i <= 5)
> > {
> > // Map degree of freedom to element degree of freedom
> > const unsigned int dof = i - 3;
> >
> > // Array of basisvalues.
> > double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
> >
> > // Declare helper variables.
> > unsigned int rr = 0;
> > unsigned int ss = 0;
> > double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
> >
> > // Compute basisvalues.
> > basisvalues[0] = 1.000000000000000;
> > basisvalues[1] = tmp0;
> > for (unsigned int r = 0; r < 1; r++)
> > {
> > rr = (r + 1)*(r + 1 + 1)/2 + 1;
> > ss = r*(r + 1)/2;
> > basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
> > }// end loop over 'r'
> > for (unsigned int r = 0; r < 2; r++)
> > {
> > for (unsigned int s = 0; s < 2 - r; s++)
> > {
> > rr = (r + s)*(r + s + 1)/2 + s;
> > basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Table(s) of coefficients.
> > static const double coefficients0[3][3] = \
> > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.000000000000000, 0.333333333333333}};
> >
> > // Compute value(s).
> > for (unsigned int r = 0; r < 3; r++)
> > {
> > values[1] += coefficients0[dof][r]*basisvalues[r];
> > }// end loop over 'r'
> > }
> >
> > }
> >
> > /// Evaluate all basis functions at given point in cell
> > virtual void evaluate_basis_all(double* values,
> > const double* coordinates,
> > const ufc::cell& c) const
> > {
> > // Helper variable to hold values of a single dof.
> > double dof_values[2] = {0.000000000000000, 0.000000000000000};
> >
> > // Loop dofs and call evaluate_basis.
> > for (unsigned int r = 0; r < 6; r++)
> > {
> > evaluate_basis(r, dof_values, coordinates, c);
> > for (unsigned int s = 0; s < 2; s++)
> > {
> > values[r*2 + s] = dof_values[s];
> > }// end loop over 's'
> > }// end loop over 'r'
> > }
> >
> > /// 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 * 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 K_00 = J_11 / detJ;
> > const double K_01 = -J_01 / detJ;
> > const double K_10 = -J_10 / detJ;
> > const double K_11 = J_00 / detJ;
> >
> > // Compute constants
> > const double C0 = x[1][0] + x[2][0];
> > const double C1 = x[1][1] + x[2][1];
> >
> > // Get coordinates and map to the reference (FIAT) element
> > double X = (J_01*(C1 - 2.0*coordinates[1]) + J_11*(2.0*coordinates[0] - C0)) / detJ;
> > double Y = (J_00*(2.0*coordinates[1] - C1) + J_10*(C0 - 2.0*coordinates[0])) / detJ;
> >
> > // Compute number of derivatives.
> > unsigned int num_derivatives = 1;
> > for (unsigned int r = 0; r < n; r++)
> > {
> > num_derivatives *= 2;
> > }// end loop over 'r'
> >
> > // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
> > unsigned int **combinations = new unsigned int *[num_derivatives];
> > for (unsigned int row = 0; row < num_derivatives; row++)
> > {
> > combinations[row] = new unsigned int [n];
> > for (unsigned int col = 0; col < n; col++)
> > combinations[row][col] = 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] = {{K_00, K_01}, {K_10, K_11}};
> >
> > // 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. Assuming that values is always an array.
> > for (unsigned int r = 0; r < 2*num_derivatives; r++)
> > {
> > values[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > if (0 <= i && i <= 2)
> > {
> > // Map degree of freedom to element degree of freedom
> > const unsigned int dof = i;
> >
> > // Array of basisvalues.
> > double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
> >
> > // Declare helper variables.
> > unsigned int rr = 0;
> > unsigned int ss = 0;
> > double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
> >
> > // Compute basisvalues.
> > basisvalues[0] = 1.000000000000000;
> > basisvalues[1] = tmp0;
> > for (unsigned int r = 0; r < 1; r++)
> > {
> > rr = (r + 1)*(r + 1 + 1)/2 + 1;
> > ss = r*(r + 1)/2;
> > basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
> > }// end loop over 'r'
> > for (unsigned int r = 0; r < 2; r++)
> > {
> > for (unsigned int s = 0; s < 2 - r; s++)
> > {
> > rr = (r + s)*(r + s + 1)/2 + s;
> > basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Table(s) of coefficients.
> > static const double coefficients0[3][3] = \
> > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.000000000000000, 0.333333333333333}};
> >
> > // Tables of derivatives of the polynomial base (transpose).
> > static const double dmats0[3][3] = \
> > {{0.000000000000000, 0.000000000000000, 0.000000000000000},
> > {4.898979485566356, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 0.000000000000000}};
> >
> > static const double dmats1[3][3] = \
> > {{0.000000000000000, 0.000000000000000, 0.000000000000000},
> > {2.449489742783178, 0.000000000000000, 0.000000000000000},
> > {4.242640687119285, 0.000000000000000, 0.000000000000000}};
> >
> > // Compute reference derivatives.
> > // Declare pointer to array of derivatives on FIAT element.
> > double *derivatives = new double[num_derivatives];
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > derivatives[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Declare derivative matrix (of polynomial basis).
> > double dmats[3][3] = \
> > {{1.000000000000000, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 1.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 1.000000000000000}};
> >
> > // Declare (auxiliary) derivative matrix (of polynomial basis).
> > double dmats_old[3][3] = \
> > {{1.000000000000000, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 1.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 1.000000000000000}};
> >
> > // Loop possible derivatives.
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > // Resetting dmats values to compute next derivative.
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > dmats[t][u] = 0.000000000000000;
> > if (t == u)
> > {
> > dmats[t][u] = 1.000000000000000;
> > }
> >
> > }// end loop over 'u'
> > }// end loop over 't'
> >
> > // Looping derivative order to generate dmats.
> > for (unsigned int s = 0; s < n; s++)
> > {
> > // Updating dmats_old with new values and resetting dmats.
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > dmats_old[t][u] = dmats[t][u];
> > dmats[t][u] = 0.000000000000000;
> > }// end loop over 'u'
> > }// end loop over 't'
> >
> > // Update dmats using an inner product.
> > if (combinations[r][s] == 0)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > for (unsigned int tu = 0; tu < 3; tu++)
> > {
> > dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
> > }// end loop over 'tu'
> > }// end loop over 'u'
> > }// end loop over 't'
> > }
> >
> > if (combinations[r][s] == 1)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > for (unsigned int tu = 0; tu < 3; tu++)
> > {
> > dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
> > }// end loop over 'tu'
> > }// end loop over 'u'
> > }// end loop over 't'
> > }
> >
> > }// end loop over 's'
> > for (unsigned int s = 0; s < 3; s++)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
> > }// end loop over 't'
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Transform derivatives back to physical element
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > for (unsigned int s = 0; s < num_derivatives; s++)
> > {
> > values[r] += transform[r][s]*derivatives[s];
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Delete pointer to array of derivatives on FIAT element
> > delete [] derivatives;
> >
> > // Delete pointer to array of combinations of derivatives and transform
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > delete [] combinations[r];
> > }// end loop over 'r'
> > delete [] combinations;
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > delete [] transform[r];
> > }// end loop over 'r'
> > delete [] transform;
> > }
> >
> > if (3 <= i && i <= 5)
> > {
> > // Map degree of freedom to element degree of freedom
> > const unsigned int dof = i - 3;
> >
> > // Array of basisvalues.
> > double basisvalues[3] = {0.000000000000000, 0.000000000000000, 0.000000000000000};
> >
> > // Declare helper variables.
> > unsigned int rr = 0;
> > unsigned int ss = 0;
> > double tmp0 = (1.000000000000000 + Y + 2.000000000000000*X)/2.000000000000000;
> >
> > // Compute basisvalues.
> > basisvalues[0] = 1.000000000000000;
> > basisvalues[1] = tmp0;
> > for (unsigned int r = 0; r < 1; r++)
> > {
> > rr = (r + 1)*(r + 1 + 1)/2 + 1;
> > ss = r*(r + 1)/2;
> > basisvalues[rr] = basisvalues[ss]*(0.500000000000000 + r + Y*(1.500000000000000 + r));
> > }// end loop over 'r'
> > for (unsigned int r = 0; r < 2; r++)
> > {
> > for (unsigned int s = 0; s < 2 - r; s++)
> > {
> > rr = (r + s)*(r + s + 1)/2 + s;
> > basisvalues[rr] *= std::sqrt((0.500000000000000 + r)*(1.000000000000000 + r + s));
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Table(s) of coefficients.
> > static const double coefficients0[3][3] = \
> > {{0.471404520791032, -0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.288675134594813, -0.166666666666667},
> > {0.471404520791032, 0.000000000000000, 0.333333333333333}};
> >
> > // Tables of derivatives of the polynomial base (transpose).
> > static const double dmats0[3][3] = \
> > {{0.000000000000000, 0.000000000000000, 0.000000000000000},
> > {4.898979485566356, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 0.000000000000000}};
> >
> > static const double dmats1[3][3] = \
> > {{0.000000000000000, 0.000000000000000, 0.000000000000000},
> > {2.449489742783178, 0.000000000000000, 0.000000000000000},
> > {4.242640687119285, 0.000000000000000, 0.000000000000000}};
> >
> > // Compute reference derivatives.
> > // Declare pointer to array of derivatives on FIAT element.
> > double *derivatives = new double[num_derivatives];
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > derivatives[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Declare derivative matrix (of polynomial basis).
> > double dmats[3][3] = \
> > {{1.000000000000000, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 1.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 1.000000000000000}};
> >
> > // Declare (auxiliary) derivative matrix (of polynomial basis).
> > double dmats_old[3][3] = \
> > {{1.000000000000000, 0.000000000000000, 0.000000000000000},
> > {0.000000000000000, 1.000000000000000, 0.000000000000000},
> > {0.000000000000000, 0.000000000000000, 1.000000000000000}};
> >
> > // Loop possible derivatives.
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > // Resetting dmats values to compute next derivative.
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > dmats[t][u] = 0.000000000000000;
> > if (t == u)
> > {
> > dmats[t][u] = 1.000000000000000;
> > }
> >
> > }// end loop over 'u'
> > }// end loop over 't'
> >
> > // Looping derivative order to generate dmats.
> > for (unsigned int s = 0; s < n; s++)
> > {
> > // Updating dmats_old with new values and resetting dmats.
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > dmats_old[t][u] = dmats[t][u];
> > dmats[t][u] = 0.000000000000000;
> > }// end loop over 'u'
> > }// end loop over 't'
> >
> > // Update dmats using an inner product.
> > if (combinations[r][s] == 0)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > for (unsigned int tu = 0; tu < 3; tu++)
> > {
> > dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
> > }// end loop over 'tu'
> > }// end loop over 'u'
> > }// end loop over 't'
> > }
> >
> > if (combinations[r][s] == 1)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > for (unsigned int u = 0; u < 3; u++)
> > {
> > for (unsigned int tu = 0; tu < 3; tu++)
> > {
> > dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
> > }// end loop over 'tu'
> > }// end loop over 'u'
> > }// end loop over 't'
> > }
> >
> > }// end loop over 's'
> > for (unsigned int s = 0; s < 3; s++)
> > {
> > for (unsigned int t = 0; t < 3; t++)
> > {
> > derivatives[r] += coefficients0[dof][s]*dmats[s][t]*basisvalues[t];
> > }// end loop over 't'
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Transform derivatives back to physical element
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > for (unsigned int s = 0; s < num_derivatives; s++)
> > {
> > values[num_derivatives + r] += transform[r][s]*derivatives[s];
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Delete pointer to array of derivatives on FIAT element
> > delete [] derivatives;
> >
> > // Delete pointer to array of combinations of derivatives and transform
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > delete [] combinations[r];
> > }// end loop over 'r'
> > delete [] combinations;
> > for (unsigned int r = 0; r < num_derivatives; r++)
> > {
> > delete [] transform[r];
> > }// end loop over 'r'
> > 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
> > {
> > // Compute number of derivatives.
> > unsigned int num_derivatives = 1;
> > for (unsigned int r = 0; r < n; r++)
> > {
> > num_derivatives *= 2;
> > }// end loop over 'r'
> >
> > // Helper variable to hold values of a single dof.
> > double *dof_values = new double[2*num_derivatives];
> > for (unsigned int r = 0; r < 2*num_derivatives; r++)
> > {
> > dof_values[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Loop dofs and call evaluate_basis_derivatives.
> > for (unsigned int r = 0; r < 6; r++)
> > {
> > evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
> > for (unsigned int s = 0; s < 2*num_derivatives; s++)
> > {
> > values[r*2*num_derivatives + s] = dof_values[s];
> > }// end loop over 's'
> > }// end loop over 'r'
> >
> > // Delete pointer.
> > delete [] dof_values;
> > }
> >
> > /// 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
> > {
> > // Declare variables for result of evaluation.
> > double vals[1];
> >
> > // Declare variable for physical coordinates.
> > double y[2];
> > const double * const * x = c.coordinates;
> > switch (i)
> > {
> > case 0:
> > {
> > y[0] = x[0][0];
> > y[1] = x[0][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > case 1:
> > {
> > y[0] = x[1][0];
> > y[1] = x[1][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > case 2:
> > {
> > y[0] = x[2][0];
> > y[1] = x[2][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > case 3:
> > {
> > y[0] = x[0][0];
> > y[1] = x[0][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > case 4:
> > {
> > y[0] = x[1][0];
> > y[1] = x[1][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > case 5:
> > {
> > y[0] = x[2][0];
> > y[1] = x[2][1];
> > f.evaluate(vals, y, c);
> > return vals[0];
> > break;
> > }
> > }
> >
> > return 0.000000000000000;
> > }
> >
> > /// 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
> > {
> > // Declare variables for result of evaluation.
> > double vals[1];
> >
> > // Declare variable for physical coordinates.
> > double y[2];
> > const double * const * x = c.coordinates;
> > y[0] = x[0][0];
> > y[1] = x[0][1];
> > f.evaluate(vals, y, c);
> > values[0] = vals[0];
> > y[0] = x[1][0];
> > y[1] = x[1][1];
> > f.evaluate(vals, y, c);
> > values[1] = vals[0];
> > y[0] = x[2][0];
> > y[1] = x[2][1];
> > f.evaluate(vals, y, c);
> > values[2] = vals[0];
> > y[0] = x[0][0];
> > y[1] = x[0][1];
> > f.evaluate(vals, y, c);
> > values[3] = vals[0];
> > y[0] = x[1][0];
> > y[1] = x[1][1];
> > f.evaluate(vals, y, c);
> > values[4] = vals[0];
> > y[0] = x[2][0];
> > y[1] = x[2][1];
> > f.evaluate(vals, y, c);
> > values[5] = vals[0];
> > }
> >
> > /// Interpolate vertex values from dof values
> > virtual void interpolate_vertex_values(double* vertex_values,
> > const double* dof_values,
> > const ufc::cell& c) const
> > {
> > // Evaluate function and change variables
> > vertex_values[0] = dof_values[0] + dof_values[3];
> > vertex_values[1] = dof_values[1] + dof_values[4];
> > vertex_values[2] = dof_values[2] + dof_values[5];
> > }
> >
> > /// Return the number of sub elements (for a mixed element)
> > virtual unsigned int num_sub_elements() const
> > {
> > return 0;
> > }
> >
> > /// 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 0;
> > }
> >
> > };
> >
> > /// This class defines the interface for a local-to-global mapping of
> > /// degrees of freedom (dofs).
> >
> >
> > class poisson_dof_map_0: public ufc::dof_map
> > {
> > private:
> >
> > unsigned int _global_dimension;
> >
> > public:
> >
> > /// Constructor
> > poisson_dof_map_0( ) :ufc::dof_map()
> > {
> > _global_dimension = 0;
> > }
> > /// Destructor
> > virtual ~poisson_dof_map_0()
> > {
> > // Do nothing
> > }
> >
> > /// Return a string identifying the dof map
> > virtual const char* signature() const
> > {
> > return "FFC dofmap 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
> > {
> > switch (d)
> > {
> > case 0:
> > {
> > return 1;
> > break;
> > }
> > case 1:
> > {
> > return 0;
> > break;
> > }
> > case 2:
> > {
> > return 0;
> > break;
> > }
> > }
> >
> > return 0;
> > }
> >
> > /// 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
> > {
> > if (d > 2)
> > {
> > throw std::runtime_error("d is larger than dimension (2)");
> > }
> >
> > switch (d)
> > {
> > case 0:
> > {
> > if (i > 2)
> > {
> > throw std::runtime_error("i is larger than number of entities (2)");
> > }
> >
> > switch (i)
> > {
> > case 0:
> > {
> > dofs[0] = 0;
> > break;
> > }
> > case 1:
> > {
> > dofs[0] = 1;
> > break;
> > }
> > case 2:
> > {
> > dofs[0] = 2;
> > break;
> > }
> > }
> >
> > break;
> > }
> > case 1:
> > {
> >
> > break;
> > }
> > case 2:
> > {
> >
> > break;
> > }
> > }
> >
> > }
> >
> > /// 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 0;
> > }
> >
> > /// 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 0;
> > }
> >
> > };
> >
> > /// This class defines the interface for a local-to-global mapping of
> > /// degrees of freedom (dofs).
> >
> >
> > class poisson_dof_map_1: public ufc::dof_map
> > {
> > private:
> >
> > unsigned int _global_dimension;
> > const std::vector<const pum::GenericPUM*>& pums;
> > public:
> >
> > /// Constructor
> > poisson_dof_map_1( const std::vector<const pum::GenericPUM*>& pums) :ufc::dof_map() , pums(pums)
> > {
> > _global_dimension = 0;
> > }
> > /// Destructor
> > virtual ~poisson_dof_map_1()
> > {
> > // Do nothing
> > }
> >
> > /// Return a string identifying the dof map
> > virtual const char* signature() const
> > {
> > return "FFC dofmap for EnrichedElement(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), ElementRestriction(FiniteElement('Lagrange', Cell('triangle', 1, Space(2)), 1), Measure('surface', 0, None)))";
> > }
> >
> > /// 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 2;
> > }
> >
> > /// Return the number of dofs associated with each cell entity of dimension d
> > virtual unsigned int num_entity_dofs(unsigned int d) const
> > {
> > switch (d)
> > {
> > case 0:
> > {
> > return 1;
> > break;
> > }
> > case 1:
> > {
> > return 0;
> > break;
> > }
> > case 2:
> > {
> > return 0;
> > break;
> > }
> > }
> >
> > return 0;
> > }
> >
> > /// 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;
> > 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
> > {
> > if (d > 2)
> > {
> > throw std::runtime_error("d is larger than dimension (2)");
> > }
> >
> > switch (d)
> > {
> > case 0:
> > {
> > if (i > 2)
> > {
> > throw std::runtime_error("i is larger than number of entities (2)");
> > }
> >
> > switch (i)
> > {
> > case 0:
> > {
> > dofs[0] = 0;
> > break;
> > }
> > case 1:
> > {
> > dofs[0] = 1;
> > break;
> > }
> > case 2:
> > {
> > dofs[0] = 2;
> > break;
> > }
> > }
> >
> > break;
> > }
> > case 1:
> > {
> >
> > break;
> > }
> > case 2:
> > {
> >
> > break;
> > }
> > }
> >
> > }
> >
> > /// 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 0;
> > }
> >
> > /// 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 0;
> > }
> >
> > };
> >
> > /// 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_cell_integral_0_0: public ufc::cell_integral
> > {
> > const std::vector<const pum::GenericPUM*>& pums;
> > mutable std::vector <double> Aa;
> >
> > /// 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 K_00 = J_11 / detJ;
> > const double K_01 = -J_01 / detJ;
> > const double K_10 = -J_10 / detJ;
> > const double K_11 = J_00 / detJ;
> >
> > // Set scale factor
> > const double det = std::abs(detJ);
> >
> > // Array of quadrature weights.
> > static const double W1 = 0.500000000000000;
> > // Quadrature points on the UFC reference element: (0.333333333333333, 0.333333333333333)
> >
> > // Value of basis functions at quadrature points.
> > static const double FE0_D01[1][6] = \
> > {{-1.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000}};
> >
> > static const double FE0_D10[1][6] = \
> > {{-1.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000}};
> >
> > static const double FE1[1][3] = \
> > {{0.333333333333333, 0.333333333333333, 0.333333333333333}};
> >
> >
> > // enriched local dimension of the current cell
> > unsigned int offset = pums[0]->enriched_local_dimension(c);
> >
> > // Reset values in the element tensor.
> > const unsigned int num_entries = (3 + offset)*(3 + offset);
> >
> > for (unsigned int r = 0; r < num_entries; r++)
> > {
> > A[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Compute element tensor using UFL quadrature representation
> > // Optimisations: ('optimisation', False), ('non zero columns', False), ('remove zero terms', False), ('ignore ones', False), ('ignore zero tables', False)
> >
> > // Loop quadrature points for integral.
> > // Number of operations to compute element tensor for following IP loop = 25
> > // Only 1 integration point, omitting IP loop.
> > // Coefficient declarations.
> > double F0 = 0.000000000000000;
> >
> > // Total number of operations to compute function values = 6
> > for (unsigned int r = 0; r < 3; r++)
> > {
> > F0 += FE1[0][r]*w[0][r];
> > }// end loop over 'r'
> > unsigned int m = 0;
> >
> > // Number of operations for primary indices = 19
> > for (unsigned int j = 0; j < 6; j++)
> > {
> > for (unsigned int k = 0; k < 6; k++)
> > {
> > // Number of operations to compute entry: 19
> > if (((((0 <= j && j < 3)) && ((0 <= k && k < 3)))))
> > {
> > A[m] += ((((K_00*FE0_D10[0][j] + K_10*FE0_D01[0][j]))*((K_00*FE0_D10[0][k] + K_10*FE0_D01[0][k])) + ((K_01*FE0_D10[0][j] + K_11*FE0_D01[0][j]))*((K_01*FE0_D10[0][k] + K_11*FE0_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_cell_integral_0_0( const std::vector<const pum::GenericPUM*>& pums) : ufc::cell_integral() , pums(pums)
> > {
> > // Do nothing
> > }
> >
> > /// Destructor
> > virtual ~poisson_cell_integral_0_0()
> > {
> > // 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);
> >
> >
> > // enriched local dimension of the current cell(s)
> > unsigned int offset = pums[0]->enriched_local_dimension(c);
> >
> > if (offset == 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((offset + 3)*(offset + 3), 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_finite_element_0 element_0;
> > poisson_finite_element_1 element_1;
> >
> > // Array of quadrature weights.
> > static const double W1[1] = {0.500000000000000};
> > // Quadrature points on the UFC reference element: (0.333333333333333, 0.333333333333333)
> >
> >
> > // 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 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 derivatives order 1 at the current guass point for <<CG1 on a <triangle of degree 1>> + <<CG1 on a <triangle of degree 1>>>|_{dc0}>
> > double value_0[2];
> > double table_1_D1[6][2];
> > for (unsigned int j = 0; j < 6; j++)
> > {
> > element_1.evaluate_basis_derivatives(j, 1, value_0, coordinate, c);
> > for (unsigned int k = 0; k < 2; k++)
> > table_1_D1[j][k] = value_0[k];
> > }
> >
> >
> > // Creating a table to save the values of shape functions at the current guass point for <CG1 on a <triangle of degree 1>>
> > double value_1[1];
> > double table_0_D0[3][1];
> > for (unsigned int j = 0; j < 3; 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];
> > }
> >
> >
> > // Creating a table to save the values of shape functions at the current guass point for <<CG1 on a <triangle of degree 1>> + <<CG1 on a <triangle of degree 1>>>|_{dc0}>
> > double value_2[1];
> > double table_1_D0[6][1];
> > for (unsigned int j = 0; j < 6; j++)
> > {
> > element_1.evaluate_basis(j, value_2, coordinate, c);
> > for (unsigned int k = 0; k < 1; k++)
> > table_1_D0[j][k] = value_2[k];
> > }
> > // Coefficient declarations.
> > double F0 = 0.000000000000000;
> >
> > // 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: 7
> > 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: 7
> > Aa[m*6 + n] += ((table_1_D1[j][1]*table_1_D1[k][1] + table_1_D1[j][0]*table_1_D1[k][0]))*F0*Wn1[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_cell_integral_1_0: public ufc::cell_integral
> > {
> > const std::vector<const pum::GenericPUM*>& pums;
> > mutable std::vector <double> Aa;
> >
> > /// 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, 0.090979309128011, 0.159020690871988, 0.090979309128011};
> > // Quadrature points on the UFC reference element: (0.178558728263616, 0.155051025721682), (0.075031110222608, 0.644948974278318), (0.666390246014701, 0.155051025721682), (0.280019915499074, 0.644948974278318)
> >
> > // Value of basis functions at quadrature points.
> > static const double FE0[4][6] = \
> > {{0.666390246014701, 0.178558728263616, 0.155051025721682, 0.666390246014701, 0.178558728263616, 0.155051025721682},
> > {0.280019915499074, 0.075031110222608, 0.644948974278318, 0.280019915499074, 0.075031110222608, 0.644948974278318},
> > {0.178558728263616, 0.666390246014701, 0.155051025721682, 0.178558728263616, 0.666390246014701, 0.155051025721682},
> > {0.075031110222608, 0.280019915499074, 0.644948974278318, 0.075031110222608, 0.280019915499074, 0.644948974278318}};
> >
> > static const double FE1[4][3] = \
> > {{0.666390246014701, 0.178558728263616, 0.155051025721682},
> > {0.280019915499074, 0.075031110222608, 0.644948974278318},
> > {0.178558728263616, 0.666390246014701, 0.155051025721682},
> > {0.075031110222608, 0.280019915499074, 0.644948974278318}};
> >
> >
> > // enriched local dimension of the current cell
> > unsigned int offset = pums[0]->enriched_local_dimension(c);
> >
> > // Reset values in the element tensor.
> > const unsigned int num_entries = (3 + offset);
> >
> > for (unsigned int r = 0; r < num_entries; r++)
> > {
> > A[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Compute element tensor using UFL quadrature representation
> > // Optimisations: ('optimisation', False), ('non zero columns', False), ('remove zero terms', False), ('ignore ones', False), ('ignore zero tables', False)
> >
> > // Loop quadrature points for integral.
> > // Number of operations to compute element tensor for following IP loop = 40
> > for (unsigned int ip = 0; ip < 4; ip++)
> > {
> > // Coefficient declarations.
> > double F0 = 0.000000000000000;
> >
> > // Total number of operations to compute function values = 6
> > for (unsigned int r = 0; r < 3; r++)
> > {
> > F0 += FE1[ip][r]*w[0][r];
> > }// end loop over 'r'
> > unsigned int m = 0;
> >
> > // Number of operations for primary indices = 4
> > for (unsigned int j = 0; j < 6; j++)
> > {
> > // Number of operations to compute entry: 4
> > if (((((0 <= j && j < 3)))))
> > {
> > A[m] += FE0[ip][j]*F0*W4[ip]*det;
> > ++m;
> > }
> >
> > }// end loop over 'j'
> > }// end loop over 'ip'
> > }
> >
> > public:
> >
> > /// Constructor
> > poisson_cell_integral_1_0( const std::vector<const pum::GenericPUM*>& pums) : ufc::cell_integral() , pums(pums)
> > {
> > // Do nothing
> > }
> >
> > /// Destructor
> > virtual ~poisson_cell_integral_1_0()
> > {
> > // 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);
> >
> >
> > // enriched local dimension of the current cell(s)
> > unsigned int offset = pums[0]->enriched_local_dimension(c);
> >
> > if (offset == 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((offset + 3), 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_finite_element_0 element_0;
> > poisson_finite_element_1 element_1;
> >
> > // Array of quadrature weights.
> > static const double W4[4] = {0.159020690871988, 0.090979309128011, 0.159020690871988, 0.090979309128011};
> > // Quadrature points on the UFC reference element: (0.178558728263616, 0.155051025721682), (0.075031110222608, 0.644948974278318), (0.666390246014701, 0.155051025721682), (0.280019915499074, 0.644948974278318)
> >
> >
> > // Array of quadrature points.
> > static const double P4[8] = \
> > {0.178558728263616, 0.155051025721682,
> > 0.075031110222608, 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 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 <CG1 on a <triangle of degree 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 <<CG1 on a <triangle of degree 1>> + <<CG1 on a <triangle of degree 1>>>|_{dc0}>
> > double value_1[1];
> > double table_1_D0[6][1];
> > for (unsigned int j = 0; j < 6; j++)
> > {
> > element_1.evaluate_basis(j, value_1, coordinate, c);
> > for (unsigned int k = 0; k < 1; k++)
> > table_1_D0[j][k] = value_1[k];
> > }
> > // Coefficient declarations.
> > double F0 = 0.000000000000000;
> >
> > // 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: 4
> > 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: 4
> > Aa[m] += table_1_D0[j][0]*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
> > /// exterior facet tensor corresponding to the local contribution to
> > /// a form from the integral over an exterior facet.
> >
> > class poisson_exterior_facet_integral_1_0: public ufc::exterior_facet_integral
> > {
> > const std::vector<const pum::GenericPUM*>& pums;
> > mutable std::vector <double> Aa;
> >
> > /// 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
> >
> > // Get vertices on edge
> > static unsigned int edge_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
> > 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);
> >
> >
> > // Array of quadrature weights.
> > static const double W2[2] = {0.500000000000000, 0.500000000000000};
> > // Quadrature points on the UFC reference element: (0.211324865405187), (0.788675134594813)
> >
> > // Value of basis functions at quadrature points.
> > static const double FE0_f0[2][6] = \
> > {{0.000000000000000, 0.788675134594813, 0.211324865405187, 0.000000000000000, 0.788675134594813, 0.211324865405187},
> > {0.000000000000000, 0.211324865405187, 0.788675134594813, 0.000000000000000, 0.211324865405187, 0.788675134594813}};
> >
> > static const double FE0_f1[2][6] = \
> > {{0.788675134594813, 0.000000000000000, 0.211324865405187, 0.788675134594813, 0.000000000000000, 0.211324865405187},
> > {0.211324865405187, 0.000000000000000, 0.788675134594813, 0.211324865405187, 0.000000000000000, 0.788675134594813}};
> >
> > static const double FE0_f2[2][6] = \
> > {{0.788675134594813, 0.211324865405187, 0.000000000000000, 0.788675134594813, 0.211324865405187, 0.000000000000000},
> > {0.211324865405187, 0.788675134594813, 0.000000000000000, 0.211324865405187, 0.788675134594813, 0.000000000000000}};
> >
> > static const double FE1_f0[2][3] = \
> > {{0.000000000000000, 0.788675134594813, 0.211324865405187},
> > {0.000000000000000, 0.211324865405187, 0.788675134594813}};
> >
> > static const double FE1_f1[2][3] = \
> > {{0.788675134594813, 0.000000000000000, 0.211324865405187},
> > {0.211324865405187, 0.000000000000000, 0.788675134594813}};
> >
> > static const double FE1_f2[2][3] = \
> > {{0.788675134594813, 0.211324865405187, 0.000000000000000},
> > {0.211324865405187, 0.788675134594813, 0.000000000000000}};
> >
> >
> > // enriched local dimension of the current cell
> > unsigned int offset = pums[0]->enriched_local_dimension(c);
> >
> > // Reset values in the element tensor.
> > const unsigned int num_entries = (3 + offset);
> >
> > for (unsigned int r = 0; r < num_entries; r++)
> > {
> > A[r] = 0.000000000000000;
> > }// end loop over 'r'
> >
> > // Compute element tensor using UFL quadrature representation
> > // Optimisations: ('optimisation', False), ('non zero columns', False), ('remove zero terms', False), ('ignore ones', False), ('ignore zero tables', False)
> > switch (facet)
> > {
> > case 0:
> > {
> > // Total nu
