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

Mon Sep 26 09:11:34 CDT 2022

```Hello Matt,

BR,
Xiaofeng

On Sep 26, 2022, at 20:29, Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>> wrote:

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<mailto: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<mailto: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.

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><mailto: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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