solving: Default to LU + MUMPS where possible

[wence-]

This makes the default user experience friendlier.

[colinjcotter]

Also isn't fieldsplit plus LU on the blocks only marginally better than unpreconditioned GMRES for e.g. mixed Poisson? This feels like a fool's errand ...

________________________________ From: David A. Ham <notifications@github.com> Sent: 09 July 2019 09:58:11 To: firedrakeproject/firedrake Cc: Subscribed Subject: Re: [firedrakeproject/firedrake] solving: Default to LU + MUMPS where possible (#1471) @dham commented on this pull request.

________________________________ In firedrake/solving_utils.py<#1471 (comment)>:

+ :arg arguments: arguments for the bilinear form (need to know if we have a Real block).

+ :arg defaults: Any default sets of parameters to supply.""" + parameters = dict(chain.from_iterable(d.items() for d in defaults)) + if any(isinstance(V, fsi.RealFunctionSpace) + for V in chain.from_iterable(a.function_space() for a in arguments)): + # There's a Real block, override with defaults with nest + jacobi. + parameters.update({"pc_type": "jacobi", "mat_type": "nest"}) + solver_parameters = solver_parameters or {} + mat_type = solver_parameters.get("mat_type") + pmat_type = solver_parameters.get("pmat_type") + # Allow anything, interpret "matfree" as matrix_free. + matfree = mat_type == "matfree" + pmatfree = pmat_type == "matfree" + # No preconditioner by default for matrix-free + if matfree or pmatfree: + parameters.update({"pc_type": "none"}) If you have a mixed system then even in 2D LU can get big fast and/or defeat the MUMPS memory management heuristics. Is this really a robust option? — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub<#1471?email_source=notifications&email_token=ABOSV4TD727PBHS4VFGDABLP6RHKHA5CNFSM4H6KHKAKYY3PNVWWK3TUL52HS4DFWFIHK3DMKJSXC5LFON2FEZLWNFSXPKTDN5WW2ZLOORPWSZGOB52YQRQ#discussion_r301472617>, or mute the thread<https://github.com/notifications/unsubscribe-auth/ABOSV4SJRPYIPW6QUKSAZF3P6RHKHANCNFSM4H6KHKAA>.

[wence-]

Also isn't fieldsplit plus LU on the blocks only marginally better than unpreconditioned GMRES for e.g. mixed Poisson? This feels like a fool's errand ...

The proposal is:

1. I can assemble an AIJ matrix -> use LU

2. I can't assemble an AIJ matrix (Real constraints) -> use fieldsplit + LU on the bit I can assemble + sherman-morrison.

[pefarrell]

Yes, if you have n real variables (n small, typically n = 1) then full Schur fieldsplit + LU for (1, 1) block + n iterations of GMRES on the Schur complement solves the problem exactly (in exact arithmetic).

[pefarrell]

If you have a mixed system then even in 2D LU can get big fast and/or defeat the MUMPS memory management heuristics. Is this really a robust option?

David makes a good point. I would suggest also defaulting to "mat_mumps_icntl_14": 200 (or similar).

[rckirby]

I also have frequent headaches trying to use mumps. Maybe we dodge then if we we can use the default LU (maybe with a special parameter to keep it from breaking on saddle points) in serial processor mode -- that's usually not terrible. Is there any experience with pastix? Lawrence and I used it in a paper to some effect, but I'm not sure how robust it is across a range of problems.

…

On Tue, Jul 9, 2019 at 3:30 PM Patrick E. Farrell ***@***.***> wrote: If you have a mixed system then even in 2D LU can get big fast and/or defeat the MUMPS memory management heuristics. Is this really a robust option? David makes a good point. I would suggest also defaulting to "mat_mumps_icntl_14": 200 (or similar). — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#1471?email_source=notifications&email_token=AA4XULZ55VJ45RWJCBR7NFDP6TYOJA5CNFSM4H6KHKAKYY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTDN5WW2ZLOORPWSZGODZRN3CA#issuecomment-509795720>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AA4XUL7B5KAA4PPWCJQEXY3P6TYOJANCNFSM4H6KHKAA> .

[wence-]

OK, so which of these best describes the conclusion of these discussions?

1. Yes, do this (with the better mumps options + fieldsplit/LU for problems with real blocks)
2. Yes, do this, but use superlu_dist instead of mumps (malloc! 64bit!)
3. No, continue with the current state of play.

[colinjcotter]

I think that for mixed problems we shouldn’t try to provide an LU default (except for R). On 10 Jul 2019, at 16:58, Lawrence Mitchell <notifications@github.com<mailto:notifications@github.com>> wrote: OK, so which of these best describes the conclusion of these discussions? 1. Yes, do this (with the better mumps options + fieldsplit/LU for problems with real blocks) 2. Yes, do this, but use superlu_dist instead of mumps (malloc! 64bit!) 3. No, continue with the current state of play. — You are receiving this because you commented. Reply to this email directly, view it on GitHub<#1471?email_source=notifications&email_token=ABOSV4SJ5APHDU45EHWVYULP6YBI5A5CNFSM4H6KHKAKYY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTDN5WW2ZLOORPWSZGODZT5U5Y#issuecomment-510122615>, or mute the thread<https://github.com/notifications/unsubscribe-auth/ABOSV4SIWWWEKAHU6JS5J5TP6YBI5ANCNFSM4H6KHKAA>.

[pefarrell]

I vote for option #1. With "mat_mumps_icntl_14": 200 MUMPS is almost bulletproof.

@colinjcotter No one is advocating fieldsplits when not necessary (they are necessary with real blocks because of technical limitations).

[rckirby]

If I don’t have to remember that mumps option and it’s robust, it’s fine with me.

…

Sent from my iPhone

On Jul 10, 2019, at 3:05 PM, Patrick E. Farrell ***@***.***> wrote: I vote for option #1. With "mat_mumps_icntl_14": 200 MUMPS is almost bulletproof. @colinjcotter No one is advocating fieldsplits when not necessary (they are necessary with real blocks because of technical limitations). — You are receiving this because you commented. Reply to this email directly, view it on GitHub, or mute the thread.

[wence-]

If we're happy with the proposal of options, I think this is now right. If not, I'll leave it until agreement is reached on what we want.

[pefarrell]

It would be good to have a test that just solved a problem with R-blocks.

[wence-]

I think I finally fixed all the corner cases. Let's hope tests pass.

[wence-]

Ready for review. All tests are passing now.