mat + mat_e of bilinear form

[martemyev]

Dear All,

After eliminating bc there is a mat_e sparse matrix such as mat+mat_e=full_matrix of the bilinear form. There are functions like FullMult and FullAddMult that use both mat and mat_e in the matrix-vector multiplication. I am wondering if I can get a full sparse matrix. I didn't find anything existing in the library, so I'm thinking about the following options:

const SparseMatrix &S = billiear_form.FullSpMat();

where

SparseMatrix BilinearForm::FullSpMat() const { return mat + mat_e; } // create a full matrix

Or maybe, something like this:

bilinear_form.RestoreFullMatrix(); // that would involve mat += mat_e
const SparseMatrix &S = bilinear_form.SpMat(); // existing way

Thanks,
Mikhail

[tzanio]

Hi Mikhail,

Can you provide more details about your use case?

Of the two options you are proposing, I think the second one is better, because it will also enable the use of FormLinearSystem(), at least in some case.

Cheers,
Tzanio

[martemyev]

Hi Tzanio,

My goal is to compute a dense matrix D = W^T * S * W, where S is a full matrix of a bilinear form, and W is a dense matrix each column X_i of which is a solution of the equation S*X_i = 0, where i corresponds to a boundary degree of freedom, i.e. W = DenseMatrix(fespace.GetVSize(), n_bdr_dofs). To solve many equations S*X_i = 0 I use the FormLinearSystem function, which creates mat_e, eliminates rows and columns corresponding to boundary dofs, and finalizes the matrix, so when I compute D using D = RAP(S, W);, the S matrix is not full, and I need it to be without boundary conditions applied.

What I do right now is - I compute S two times: first time - to compute W, and the second time - to compute D. That works fine, but I'm wondering if I can do it more efficiently.

Thanks,
Mikhail

[tzanio]

Hi Mikhail,

If I understand correctly, D is the Schur complement with respect to the boundary? The action of D can probably be computed more efficiently than solving the many systems, but if you need the actual dense matrix itself, than I what you are doing is certainly a valid approach.

If you want to restore the full matrix, you probably want to call

SparseMatrix * Add(const SparseMatrix & A, const SparseMatrix & B);

though depending on the sizes, this may not be more efficient than reassembly.

Hope this helps,
Tzanio

[martemyev]

Hi Tzanio,

Thank you for the reply. I do need the dense matrix W itself, so I need to construct it explicitly. I'm going to follow your advice on the computation of the full matrix using Add() function, therefore I created a pull request to get an access to the mat_e matrix.

Thank you,
Mikhail