Solving the linear system of equations using PETSc BlockSparseMatrix

[Masoud Ahmadi]

Dear All,

The following system of equations:

KQ=R

where,

were solved using BlockSparseMatrix to form tangent matrix K. It was solved by:

SparseDirectUMFPACK A_direct;
A_direct.initialize(K);

A_direct.vmult(Q_stp, R);

Now, I'm trying to run my code with MPI using PETSc/Trilinos, but the solver does not except  PETSc/Trilinos BlockSparseMatrix. How do we solve such a general system of equations?

[Bruno Turcksin]

Hi,

If you search for "block solver" here https://dealii.org/developer/doxygen/deal.II/Tutorial.html, you will see all the tutorials that use block solvers. I think that only deal.II's own solvers support BlockSparseMatrix directly.

Best,

Bruno

[Masoud Ahmadi]

Dear Bruno,

Thanks for your reply.

I had seen those before, but, unfortunately none of those solve a general PETSc/Trilinos BlockSparseMatrix problem.

[Bruno Turcksin]

They do. Take for example step-70, the matrix is a LA::MPI::BlockSparseMatrix which is a PETSc or a Trilinos BlockSpaceMatrix depending on how deal.II was configured.

Bruno

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[Masoud Ahmadi]

Thanks for the reply.

I had seen that, they solve it for the "diagonal" blocks; I want a general method. My system of equations is not like any special cases in the Tutorials.

As I said, I solve the one without Trilinos/PETSc by:

SparseDirectUMFPACK A_direct;
A_direct.initialize(K);

A_direct.vmult(Q_stp, R);

I am looking for something similar.

[Bruno Turcksin]

I am not sure what you mean by solving for diagonal blocks. The solver is general; it is the preconditioner that is block diagonal. If you want to use MPI, I assume that you have a large system. In this case, direct solvers are not very effective and you need to use an iterative solver. deal.II's iterative solvers work with any BlockSparseMatrix. The tutorials show you how to take advantage of the blocks to build a good preconditioner. If you don't want to use a preconditioner, that's fine. The code will be similar to what you have now but it will be slow.

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[Daniel Arndt]

Adding to what Bruno is saying,

If you are not taking advantage of the block structure, you should be able to treat the block matrix as "regular", i.e., non-block, matrix possibly by copying it to a corresponding non-block type.

Best,

Daniel

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[Masoud Ahmadi]

Dear Bruno and Daniel,

Thanks for your replies.

I used linear_operator and then solve the problem like step-70.

I guess there is no "Direct solver" for this situation, the one like we had for dealii BlockSparseMatrix.

Best regards,

Masoud