[petsc-users] Block preconditioning for 3d problem

[Dave Lee]

Hi Jed and Mark,

thanks for your helpful comments. Yes the nonlinear outer problem is
uncoupled between the slabs, it is only the linear inner problem where they
are coupled.

I've tried to make the slab DOFs close in memory, and also tried using a
tight tolerance on the outer KSP (1.0e-20), but without success.

You make some really good points about scaling issues Jed and Mark. This is
a solve for a global atmosphere, and each 2D slab is a horizontal layer of
the atmosphere, so the pressure (which the linear solve is for) will vary
dramatically between slabs. Perhaps I can additionally precondition the
linear problem to normalise the pressure in each slab so that they stay
close to unity.

Cheers, Dave.

On Fri, Oct 11, 2019 at 2:52 AM Mark Adams <mfadams at lbl.gov> wrote:

> I can think of a few sources of coupling in the solver: 1) line search and
> 2) Krylov, and 3) the residual test (scaling issues). You could turn
> linesearch off and use Richardson (with a fixed number of iterations) or
> exact solves as Jed suggested. As far as scaling can you use the same NL
> problem on each slab? This should fix all the problems anyway. Or, on the
> good decouple solves, if the true residual is of the same scale and *all*
> of the slabs converge well then you should be OK on scaling. If this works
> then start adding stuff back in and see what breaks it.
>
> On Thu, Oct 10, 2019 at 11:01 AM Jed Brown via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>> Dave Lee via petsc-users <petsc-users at mcs.anl.gov> writes:
>>
>> > 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.
>>
>> Is the nonlinear problem also decoupled between slabs?
>>
>> If you solve the linear problem accurately (tight tolerances on the
>> outer KSP, or global direct solve), is the outer nonlinear convergence
>> good again?  If not, test that your Jacobian is correct (it likely isn't
>> or you have inconsistent scaling leading to ill conditioning).  SNES has
>> automatic tests for that, but you aren't using SNES so you'd have to
>> write some code.
>>
>> What happens if you run the 2D problem (where convergence is currently
>> good) with much smaller subdomains (or -pc_type pbjacobi)?
>>
>> > 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.
>>
>> For convergence, you usually want the direction of tight coupling
>> (sounds like that is within slabs) to be close in memory.
>>
>> In general, use -ksp_monitor_true_residual -ksp_converged_reason.
>>
>> > I'm configuring the 3D inner linear solver as
>> >
>> > KSPGetPC(ksp, &pc);
>> > PCSetType(pc, PCBJACOBI);
>> > PCBJacobiSetLocalBlocks(pc, num_slabs, NULL);
>> > 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);
>> > }
>> >
>> > 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.
>>
>
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