Hello I am trying to speed up a two dimensional linear elasticity problem with isotropic and heterogeneous properties. It is a topology optimization problem, therefore some regions have an almost zero stiffness whereas other regions have a higher value, making the matrix ill-conditioned. So far, from having searched mail lists on similar problems, I have come up with the following CL options to pass to the petsc solver (two dimensional problem):
-ksp_type cg -pc_type fieldsplit -pc_fieldsplit_block_size 2 -fieldsplit_pc_type hypre -fieldsplit_pc_hypre_type boomeramg -fieldsplit_pc_hypre_boomeramg_strong_threshold 0.7 -pc_fieldsplit_0 0,1 -pc_fieldsplit_type symmetric_multiplicative -ksp_atol 1e-10 It works reasonably well and shows similar number of iterations for different levels of refinement. However, it does not converge when I use the same options for KSPSolveTranspose(). I obtain DIVERGED_INDEFINITE_PC after three iterations. I believe this has to do with the field split, but I do not where to start. I am using libMesh which interfaces with petsc through the file petsc_linear solver.C (http://libmesh.github.io/doxygen/classlibMesh_1_1PetscLinearSolver.html#a4e66cc138b52e80e93a75e55315245ee) The KSPSolveTranspose() is called in adjoint_solve(). Changing that to KSPSolve() solves the issue and to me it is not a problem because my matrix is symmetric, but I don’t want to have to change it in the libMesh source code. So the question is, why do those CL options not work for the KSPSolveTranspose() despite having a symmetric matrix? Thanks
