Hello FreeFEM developers,

I have a multiphysics problem which results in a 9x9 block matrix system. Each of these blocks is itself composed of several small sub-blocks which correspond to different meshes and physics. Currently, I am using PETSc to solve this system based on a block preconditioner using the fieldsplit framework. In this approach, each of the 9 blocks along the diagonal is factorized one after the other using MUMPS. Note that each block is quite reasonably sized for direct methods and the overall system has ~5 million DoF.

I have confirmed that this approach works, but I would like to accelerate the preconditioner factorization step. It seems to me that a significant improvement could be attained by attacking the factorizations for the blocks along the diagonal in parallel. However, I am not sure how to tell PETSc to do this.

The relevant commands I am currently using are below. Is there a command I can add to my ``ssparams’’ variable to make PETSc push the factorization steps to different (groups of) processors? Thanks in advance!

```
real[int] ffields(N*NDOF); // create matrix numbering for fieldsplit
string[int] nnames(N); // N is number of blocks, NDOF is number of DOF per block
for (int n = 0; n < N; n++){
ffields(n*NDOF:(n+1)*NDOF - 1) = real(n+1);
nnames[n] = "block" + n;
}
string ssparams = "-ksp_type gmres -pc_type fieldsplit -pc_fieldsplit_type multiplicative ";
for (int n = 0; n <= N; n++){
ssparams = ssparams + "-fieldsplit_" + nnames[n] + "_pc_type lu ";
ssparams = ssparams + "-fieldsplit_" + nnames[n] + "_ksp_type preonly ";
ssparams = ssparams + "-fieldsplit_" + nnames[n] + "_pc_factor_mat_solver_type mumps ";
}
matrix A;
funcA(A); // build A matrix (consisting of all 9x9 blocks)
Mat dA = A; // convert to PETSc Mat
set(dA, sparams = ssparams, fields = ffields, names = nnames);
real[int] b(N*NDOF);
funcb(b); // build RHS vector
real[int] x = dA^-1*b // solve Ax=b
```