[petsc-users] GMRES with matrix-free method and preconditioning matrix for higher performance.

[Choi Kyungjun]

Thank you very much again Matt.

Just another simple question.

2016-08-31 20:00 GMT+09:00 Matthew Knepley <knepley at gmail.com>:

> On Wed, Aug 31, 2016 at 5:46 AM, Choi Kyungjun <kyungjun.choi92 at gmail.com>
> wrote:
>
>> Thanks Matt.
>>
>> I really appreciate your help every time.
>>
>>
>> I think I forgot mentioning code info again.
>>
>> 1)
>> I'm working on 2-D/3-D Compressible Euler equation solver, which is
>> completely hyperbolic system.
>>
>
> Okay, then MG is out. I would start by using a sparse direct solver, like
> SuperLU. Then for parallelism
> you could use ASM, and as the subsolver use SuperLU, so something like
>
>   -ksp_type gmres -pc_type asm -sub_pc_type superlu
>
> You could get more sophisticated by
>
>   - Trying to have blocks bigger than 1 process and using SuperLU_dist
>
>   - Splitting up the fields using PCFIELDSPLIT. There are indications that
> solving one of the fields first
>     can really help convergence. I am thinking of the work of David Keyes
> and LuLu Liu on MSM methods.
>

For the above part,

It's not compatible with -snes_mf  command line option, is it?

I applied cmd line options like below
*-snes_mf     -ksp_type  gmres     -pc_type asm     -sub_pc_type superlu
  -snes_view     -snes_monitor     -ksp_monitor    -snes_converged_reason
 -ksp_converged_reason*


and my code flows like this

*- call SNESCreate(PETSC_COMM_WORLD, Mixt%snes, ier)*
*- call SNESSetFunction(Mixt%snes, Mixt%r, FormFunction, userctx, ier)*
*- call SNESSetFromOptions(Mixt%snes, ier)*
*- call SNESGetKSP(Mixt%snes, ksp, ier)*
*- call KSPGetPC(ksp, pc, ier)*

*- call KSPSetFromOptions(ksp, ier)*
*- call PCSetFromOptions(pc, ier)*






>
>
>> 2)
>> And I'm trying to implement some implicit time scheme for convergence of
>> my steady state problem.
>>
>> I used LUSGS implicit scheme before, but these days GMRES implicit scheme
>> is popular for quadratic convergence characteristics.
>>
>
> I am not sure I understand here. Nothing about GMRES is quadratic.
> However, Newton's method can be quadratic
> if your initial guess is good, and GMRES could be part of a solver for
> that.
>
>
>> For implicit time scheme, it is just same as matrix inversion, so I
>> started PETSc library for GMRES, which is one of the greatest mathematical
>> library.
>>
>>
>> 3)
>> As I'm using different numerical convective flux scheme (e.g. Roe's FDS,
>> AUSM, etc), it would be really time consuming to derive Jacobian matrix for
>> each scheme.
>>
>
> Yes. However, the preconditioner matrix only needs to be approximate. I
> think you should derive one for the easiest flux scheme and
> always use that. The important thing is to couple the unknowns which
> influence each other, rather than the precise method of influence.
>
>   Thanks,
>
>       Matt
>
>
>> So I was fascinated by matrix-free method (I didn't completely understand
>> this method back then), and I implemented GMRES with no preconditioning
>> matrix with your help.
>>
>> After that, I wanted to ask you about any accelerating methods for my
>> GMRES condition.
>>
>> I will try applying CHEBY preconditioner as you mentioned first (even if
>> its performance wouldn't be that good).
>>
>> In order to constitute user-provided preconditioning matrix, could you
>> tell me any similar examples?
>>
>>
>> Thanks again.
>>
>> Your best,
>>
>> Kyungjun.
>>
>>
>> 2016-08-31 19:07 GMT+09:00 Matthew Knepley <knepley at gmail.com>:
>>
>>> On Wed, Aug 31, 2016 at 3:49 AM, Choi Kyungjun <
>>> kyungjun.choi92 at gmail.com> wrote:
>>>
>>>> Dear Petsc.
>>>>
>>>> I am implementing Petsc library for my CFD flow code.
>>>>
>>>> Thanks to Matt, I got what I wanted last week.
>>>>
>>>> It was the GMRES with matrix-free method, no preconditioning matrix and
>>>> command line options are below.
>>>>
>>>> *-snes_mf    -pc_type none    -..monitor   -..converged_reason*
>>>>
>>>> The solve worked, but performed very poorly.
>>>>
>>>>
>>>> I learned that the efficiency of Krylov-subspace methods depends
>>>> strongly depends on a good preconditioner.
>>>>
>>>> And in the Petsc manual, the matrix-free method is allowed only with no
>>>> preconditioning, a user-provided preconditioner matrix, or a user-provided
>>>> preconditioner shell.
>>>>
>>>>
>>>> Here are my questions.
>>>>
>>>> 1) To improve the solver performance using GMRES, is there any way
>>>> using snes_mf without preconditioning matrix?
>>>>
>>>
>>> Not really. The CHEBY preconditioner will work without an explicit
>>> matrix, however its not great by itself.
>>>
>>>
>>>> 2) For user-provided preconditioner matrix, I saw some example codes
>>>> that provide approx. Jacobian matrix as preconditioner matrix. But this
>>>> means that I should derive approx. Jacobian mat for system, am I right?
>>>>
>>>
>>> Yes.
>>>
>>>
>>>> 3) I'd like to know which is the fastest way to solve with GMRES
>>>> method. Could you tell me or let me know any other examples?
>>>>
>>>
>>> 1) The solve depends greatly on the physics/matrix you are using.
>>> Without knowing that, we can't say anything. For example, is
>>> the system elliptic? If so, then using Multigrid (MG) is generally a
>>> good idea.
>>>
>>> 2) In general, I think its a mistake to think of GMRES or any KSP as a
>>> solver. We should think of them as accelerators for solvers,
>>> as they were originally intended. For example, MG is a good solver for
>>> elliptic CFD equations, as long as you somehow deal with
>>> incompressibility. Then you can use GMRES to cleanup some things you
>>> miss when implementing your MG solver.
>>>
>>> 3) The best thing to do in this case is to look at the literature, which
>>> is voluminous, and find the solver you want to implement. PETSc
>>> really speeds up the actually implementation and testing.
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Thank you very much for your help.
>>>>
>>>> Sincerely,
>>>>
>>>> Kyungjun.
>>>>
>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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