dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Tue, Sep 30, 2008 at 05:03:38PM +0200, Evan Lezar wrote:
> 
> 
> On Tue, Sep 30, 2008 at 3:22 PM, Matthew Knepley <knepley@xxxxxxxxx> wrote:
> 
>     On Tue, Sep 30, 2008 at 4:46 AM, Evan Lezar <evanlezar@xxxxxxxxx> wrote:
>     > On Tue, Sep 30, 2008 at 10:53 AM, Jed Brown <jed@xxxxxxxx> wrote:
>     >>
>     >> On Tue 2008-09-30 10:48, Evan Lezar wrote:
>     >> > I was wondering what the best way is to concatenate PETSc matrices?  I
>     >> > am
>     >> > currently using the set() method, but this takes quite a bit of time.
>     >>
>     >> What are you trying to do?  You should probably preallocate the full
>     >> matrix from the beginning.
>     >
>     > I am assembling a number of submatrices.  And then trying to concatenate
>     > them to form one large eigensystem.  I do pre-allocate the matrix that I
>     > want to place the entries in.
> 
>     I agree with Jed. The best way to do this is to assemble the full system
>     matrix,
>     and then if submatrices are required, you pull them out using
>     MatGetSubmatrix().
> 
>     The only situation I can see that is different is in some algorithms
>     like FETI in
>     which submatrices are unassembled. Then you would have to use a MATIS
>     structure, or something else depending on your algorithm.
> 
>      Matt
> 
>     > It may be that I would be able to use mixed elements to do the same
>     thing.
>     > I will see if I can get a code snippet together.
>     >
>     > Evan
>     >
> 
> 
> I am trying to model the transverse and axial components of the electric field
> in a waveguide - using Nededec vector elements and Lagrange elements
> respectively.
> 
> Consider the code snippet below that describes the matrices:
> 
> ====================================
> 
>     vector_element = FiniteElement("Nedelec", "triangle", 1)
>     nodal_element = FiniteElement("Lagrange", "triangle", 1)
>    
>     N_v = TestFunction(vector_element);
>     N_u = TrialFunction(vector_element);
>    
>     L_v = TestFunction(nodal_element);
>     L_u = TrialFunction(nodal_element);
>    
>     """ define the forms """
>     a_tt = dot(curl_t(N_v), curl_t(N_u))*dx - dot(N_v, N_u)*dx
>    
>     b_tt = dot(N_v, N_u)*dx
>     b_tz = dot(N_v, grad(L_u))*dx
>     b_zt = dot(grad(L_v), N_u)*dx
>    
>     b_zz = dot(grad(L_v), grad(L_u))*dx - L_v*L_u*dx
>                        
>     """ define the mesh """
>     width = 22.86e-3
>     height = 10.16e-3
>     mesh = Rectangle(0, width, 0, height, 1, 2, 0)
>     mesh.refine()
>     mesh.refine()
>     c = 2.99792458e8
>    
>     """ Assemble the sub-matrices """
>    
>     B_tt = PETScMatrix()
>     assemble(b_tt, mesh, tensor=B_tt)
>     B_tz = assemble(b_tz, mesh)
>     B_zt = assemble(b_zt, mesh)
>     B_zz = assemble(b_zz, mesh)
>    
>     A_tt = PETScMatrix()
>     assemble((a_tt, mesh, tensor=A_tt)
> 
> =============================
> I then need to construct the following matrices to solve an eigensystem:
> 
> L = [ B_tt,  B_tz ]
>        [ B_zt,  B_zz ]
> 
> and
> 
> R = [ B_tt + k*A_tt, B_tz  ]
>        [ B_zt,                B_zz ]
> 
> 
> 
> So, is someone knows how I can define a mixed element that achieves the same it
> would be much appreciated, or a means to concatenate the matrices effectively.
> 
> Evan

Just do

  vector_element = FiniteElement("Nedelec", "triangle", 1)
  nodal_element = FiniteElement("Lagrange", "triangle", 1)

  element = vector_element + nodal_element

  (N_v, L_v) = TestFunctions(element)
  (N_v, L_u) = TrialFunctions(element)

  b = dot(N_v, N_u)*dx + dot(N_v, grad(L_u))*dx + dot(grad(L_v), N_u)*dx + dot(grad(L_v), grad(L_u))*dx - L_v*L_u*dx

  B = assemble(B)

-- 
Anders

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