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> 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> 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> 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 <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/>