Hello Matt, Many thanks for your suggestion.
BR, Xiaofeng On Sep 26, 2022, at 20:29, Matthew Knepley <knep...@gmail.com<mailto:knep...@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 <tlan...@hotmail.com<mailto:tlan...@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 <j...@jedbrown.org<mailto:j...@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 <tlan...@hotmail.com<mailto:tlan...@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 <tlan...@hotmail.com<mailto:tlan...@hotmail.com><mailto:tlan...@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/>
