[petsc-users] Solve Linear System with Field Split Preconditioner

[Matthew Knepley]

Another option are the PCPATCH solvers for multigrid, as shown in this
paper: https://arxiv.org/abs/1912.08516
which I believe solves incompressible elasticity. There is an example in
PETSc for Stokes I believe.

  Thanks,

     Matt

On Mon, Sep 26, 2022 at 5:20 AM 晓峰 何 <tlanyan at hotmail.com> wrote:

> Are there other approaches to solve this kind of systems in PETSc except
> for field-split methods?
>
> Thanks,
> Xiaofeng
>
> On Sep 26, 2022, at 14:13, Jed Brown <jed at jedbrown.org> wrote:
>
> This is the joy of factorization field-split methods. The actual Schur
> complement is dense, so we represent it implicitly. A common strategy is to
> assemble the mass matrix and drop it in the 11 block of the Pmat. You can
> check out some examples in the repository for incompressible flow (Stokes
> problems). The LSC (least squares commutator) is another option. You'll
> likely find that lumping diag(A00)^{-1} works poorly because the resulting
> operator behaves like a Laplacian rather than like a mass matrix.
>
> 晓峰 何 <tlanyan at hotmail.com> writes:
>
> If assigned a preconditioner to A11 with this cmd options:
>
>   -fieldsplit_0_ksp_type gmres -fieldsplit_0_pc_type ilu
> -fieldsplit_1_ksp_type gmres -fieldsplit_1_pc_type ilu
>
> Then I got this error:
>
> "Could not locate a solver type for factorization type ILU and matrix type
> schurcomplement"
>
> How could I specify a preconditioner for A11?
>
> BR,
> Xiaofeng
>
>
> On Sep 26, 2022, at 11:02, 晓峰 何 <tlanyan at hotmail.com<
> mailto:tlanyan at hotmail.com <tlanyan at hotmail.com>>> wrote:
>
> -fieldsplit_0_ksp_type gmres -fieldsplit_0_pc_type ilu
> -fieldsplit_1_ksp_type gmres -fieldsplit_1_pc_type none
>
>
>

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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