[petsc-users] Block preconditioning for 3d problem

[Smith, Barry F.]

> On Oct 10, 2019, at 2:58 AM, Dave Lee via petsc-users <petsc-users at mcs.anl.gov> wrote:
> 
> Hi PETSc,
> 
> I have a nonlinear 3D problem for a set of uncoupled 2D slabs. (Which I ultimately want to couple once this problem is solved).
> 
> When I solve the inner linear problem for each of these 2D slabs individually (using KSPGMRES) the convergence of the outer nonlinear problem is good. However when I solve the inner linear problem as a single 3D problem (with no coupling between the 2D slabs, so the matrix is effectively a set of uncoupled blocks, one for each 2D slab) the outer nonlinear convergence degrades dramatically.
> 
> Note that I am not using SNES, just my own quasi-Newton approach for the outer nonlinear problem.
> 
> I suspect that the way to recover the convergence for the 3D coupled problem is to use some sort of PCBJACOBI or PCFIELDSPLIT preconditioner, but I'm not entirely sure. I've tried following this example:
> https://www.mcs.anl.gov/petsc/petsc-current/src/ksp/ksp/examples/tutorials/ex7.c.html
> but without any improvement in the convergence. 
> 
> On each processor the slab index is the major index and the internal slab DOF index is the minor index. The parallel decomposition is within the 2D slab dimensions only, not between slabs.

  So each slab lives on all the processes?

> 
> I'm configuring the 3D inner linear solver as

  How many processes and how many slabs are you running with? 

> 
> KSPGetPC(ksp, &pc);
> PCSetType(pc, PCBJACOBI);
> PCBJacobiSetLocalBlocks(pc, num_slabs, NULL);

    There will be num_slabs blocks per processor times the number of processors. Depending on the layout of the unknowns each block will consist of a entire local slap or each block will consist of pieces from each slap. 

> KSPSetUp(ksp);
> PCBJacobiGetSubKSP(pc, &nlocal, &first_local, &subksp);
> for(int ii = 0; ii < nlocal; ii++) {
>     KSPGetPC(subksp[ii], &subpc);
>     PCSetType(subpc, PCJACOBI);
>     KSPSetType(subksp[ii], KSPGMRES);
>     KSPSetTolerances(subksp[ii], 1.e-12, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT);
> }

  Please run the linear solver with 

    -ksp_monitor_true_residual -sub_ksp_monitor_true_residual -ksp_converged_reason -sub_ksp_converged_reason 


  Do you get huge iteration counts somewhere? 

  Next run the same thing but add -ksp_type fgmres does that change anything?

  Send all the results in an attached file.

Barry



> 
> However this does not seem to change the outer nonlinear convergence. When I run with ksp_view the local block sizes look correct - number of local 2D slab DOFs for each block on each processor.
> 
> Any ideas on what sort of KSP/PC configuration I should be using to recover the convergence of the uncoupled 2D slab linear solve for this 3D linear solve? Should I be rethinking my node indexing to help with this?
> 
> Cheers, Dave.