Passing block information into ASMStarPC and friends about firedrake

[pbrubeck]

Is the new default ordering introduced by #3435 still giving issues for saddle point patch submatrices? How is this different from a direct solve? Why do you need to construct such sophisticated solver on each patch?

[colinjcotter]

My patches are full column patches - we use ASMStarPC as a mixed system line smoother on extruded meshes. So I would like to reduce the system to see if it can speed up the solve.

[pbrubeck]

I think the options you have are not entirely right, you should use -pc_fieldsplit_detect_saddle_point https://petsc.org/main/manualpages/PC/PCFieldSplitSetDetectSaddlePoint/

[pbrubeck]

Elimination of one field via static condensation is equivalent to LU/Cholesky in the (u,p) ordering (which we now ensure)

[colinjcotter]

Right! That’s true. I wasn’t up to date with this ordering.

[pbrubeck]

Maybe try with cholmod/umfpack I think those should be the most performant for a medium-sized sequential matrix. -pc_type cholesky -pc_factor_mat_solver_type cholmod should use half of the memory/flops compared to LU and works for indefinite symmetric problems by doing LDLT.

[pbrubeck]

Also, for ASMStarPC one should specify pc_star_construct_dim, not codim that's only for Vanka and Linesmooth