I don't think you need to use multigrid for inverting the HDiv mass matrix, since it is very well conditioned. Probably CG+Jacobi already works. If 0 is the HDiv space, then can you try:

        solver_parameters={'pc_type': 'fieldsplit',
                 'pc_fieldsplit_type': 'schur',
                 'ksp_type': 'gmres',
                 'ksp_rtol':self._tolerance,
                 'pc_fieldsplit_schur_fact_type': 'FULL',
                 'pc_fieldsplit_schur_precondition': 'selfp',
                 'fieldsplit_0_ksp_type': 'cg',
                 'fieldsplit_0_pc_type': 'jacobi',
                 'fieldsplit_1_ksp_type': 'preonly',
                 'fieldsplit_1_pc_type': 'hypre',

That should use hypre's boomerAMG. Or replace the last two entries with 'fieldsplit_1_pc_type': 'gamg'. The standard AMG settings might work in your case.

From: firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk> on behalf of Andrew McRae <A.T.T.McRae@bath.ac.uk>
Sent: 15 October 2015 14:18
To: firedrake@imperial.ac.uk
Subject: Re: [firedrake] Preconditioner for Least-squares FEM

As usual, the Firedrake person in the best position to answer your question is Lawrence, but he's currently on holiday.

I won't try to answer your question, but in an old email, Lawrence suggested you try using multigrid on the blocks; e.g.

'fieldsplit_0_pc_type': 'gamg',
'fieldsplit_1_pc_type': 'gamg',

My linear solver knowledge is pretty dire, so I'll stop talking here :)

Andrew

On 15 October 2015 at 13:58, Justin Chang <jychang48@gmail.com> wrote:

I did ask them, but it went unanswered for the last 1.5 months...

Let me clarify my question a bit though, I tried using -ksp_type cg -pc_type hypre -pc_hypre_type boomeramg, but it is not supported for matnest. I added nest=False but it seems to break my solver somehow.

The only thing that works for me is -ksp_type cg -pc_type bjacobi plus MixedVectorSpaceBasis(W, ...) but the number of solver iterations increases with problem size...

Thanks,

Justin

On Thu, Oct 15, 2015 at 6:50 AM, Andrew McRae <A.T.T.McRae@bath.ac.uk> wrote:

I think the PETSc mailing list is a much better place to ask questions like this?

On 15 October 2015 at 13:47, Justin Chang <jychang48@gmail.com> wrote:

Hi all,

I am attempting to solve Darcy's equation:

u + grad[p] = 0
div[u] = f

The weak form under the least-squares finite element method (LSFEM)
looks like this:

(u + grad[p]; v + grad[q]) + div[u]*div[v] = (f; div[v])

For H(div) elements like RT0, these options worked nicely:

-ksp_type gmres
-pc_type fieldsplit
-pc_fieldsplit_type schur
-pc_fieldsplit_schur_precondition selfp
-fieldsplit_0_ksp_type preonly
-fieldsplit_0_pc_type bjacobi
-fieldsplit_0_sub_pc_type ilu
-fieldsplir_1_ksp_type preonly
-fieldsplit_1_pc_type hypre

but for the above LSFEM, it does not work (get a DIVERGED_MAX_IT error). I heard multigrid methods are good for these types of problems, so how do I tweak the above parameters?

Thanks,

Justin

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