Additional SchurComplement Feature

[Alistair Bentley]

I've been working on performance testing some new preconditioning options for NSE in Proteus. I'd like to be able to specify my own approximation for the Schur operator S that appears in the Schur complement method. I believe this can be achieved with the PETSc function MatCreateSchurComplement but I haven't found support for this in petsc4py.

I'd be happy to submit a PR adding this feature but I wanted to make sure it wasn't already something that was already in place that I just missed.

Thanks in advance,

Alistair

[Lisandro Dalcin]

No, these wrappers are missing. Contributions welcome! Thank you in advance...

PS: However, make sure MatCreateSchurComplement() is what you really need. Maybe all what you need is to define a new matrix operator with the right sizes according to the pressure space discretization. Are you planning to build an explicit, AIJ-format matrix for the preconditioner? Or maybe will you use a "matrix-free" approach? For the second case, petsc4py do have something builtin. Just let me know.

[Alistair Bentley]

Thanks for the comments.

Originally I was planning to use the matrix-free approach to build the operator, but I didn't see a way to override the default PETSc approximation to the Schur operator. After a bit of reading, it seemed to me that MatCreateSchurComplement might be able to do the trick.

Anyway, I'm going to play around with this for a bit and I'll circle back when I find a solution.

[Lisandro Dalcin]

@alistairbntl Any news? Can I close this issue?

[Alistair Bentley]

Sorry for dragging my feet on this. I've been able to achieve what I was hoping for through the ksp.pc object. That said, I keep meaning to set up MatCreateSchurComplement() function because I think it will achieve the same thing in a more transparent way. Either way, feel free to close this issue and whenever I get around to setting up MatCreateSchurComplement() I can submit the wrapper in a PR.