apply Dirichlet conditions by setting rows to I, rhs to value

For the first time, I’m looking at scikit-fem in a serious manner. Diving into it, I notice that the common way the “apply” Dirichlet conditions is to eliminate the respective entries from the matrix/rhs à la

A, b = condense(A, b, I=mesh.interior_nodes())

I on the other hand would like to see those condition applied via setting the respective rows in A to diagonal 1 and 0 otherwise plus the respective rhs entry to the value. Something like

apply_dirichlet(A, b, mesh.boundary_nodes(), vals)

perhaps. The resulting matrix has the same spectral properties as the condensed A, so the number of iterations with Krylov methods will be the same, too. Advantages of this approach include the fact that neither A nor b need to be rewritten in memory. Also, the solution will include the values of all degrees of freedom, making postprocessing easier.

[kinnala]

Something like

for i in dofs:
    matrix.data[matrix.indptr[i] : matrix.indptr[i + 1]] = 0.0

d = matrix.diagonal()
d[dofs] = 1.0

would set the rows to I, but perhaps one can do better than the python loop here. I’ve added a feature request in scipy, but the above would already work well as a makeshift solution.

Alright, I’m a little slow. You already had a solution here and it remains to vectorize it.

[gdmcbain]

Ah, of course:

backsolve = splu(A.T).solve

the left stepping matrix A is no longer symmetric so can’t just be transposed willy-nilly to avoid the

SparseEfficiencyWarning: splu requires CSC matrix format

Replacing that with backsolve = splu(A).solve makes it run O. K.