Xiaofeng, is your saddle point due to incompressibility or other constraints (like Lagrange multipliers for contact or multi-point constraints)? If incompressibility, are you working on structured or unstructured/non-nested meshes?
Matthew Knepley <knep...@gmail.com> writes: > 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/>