Rectangular matrix, constraints
Basca Jadamba
I am trying to assemble a rectangular matrix S with a property that K*U=S*A where A/U is the coefficient/solution pair in an elliptic PDE (think -div(a grad u) = f) and where K is the system matrix. S is a FullMatrix (no sparsity pattern) and it works fine on uniform meshes (correctness is checked by a norm of the difference K*U-S*A). I am not able to get a correct matrix on adaptively refined meshes and it has probably to do something with the constraints for U and A. I have this issue for a scalar (problem above) and a vector problem (linear elasticity). Something like this is used for the assembling step:
constraints_row.distribute_local_to_global(cell_matrix,
local_dof_indices_row,
constraints_col,
local_dof_indices_col,
S);
Can anyone give me a suggestion where the problem could be or where I should look in the documentation?
Wolfgang Bangerth
if you solve the linear system for U, you should *always* have that
|| KU - SA ||
is small, simply by virtue of having solved the linear system. If the norm is
not small, then you haven't solved the linear system.
The way I tend to debug this kind of thing is to make the situation as small
as possible. In your case, this would mean using lowest order elements,
choosing the mesh to be a 2x2 mesh where you refine one cell, and then you can
use a piece of paper to enumerate all degrees of freedom and compute matrix
and vector elements by hand. For this situation, you have only 14 DoFs -- few
enough that things fit on a single page with a bit of work.
Best
W.
--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/