[petsc-users] Change Amat in FormJacobian

[Dave May]

Hi Anton,

On Mon, 14 Jun 2021 at 14:47, Anton Popov <popov at uni-mainz.de> wrote:

> Hi Barry & Matt,
>
> thanks for your quick response. These options were exactly what I needed
> and expected:
>
> -pc_mg_galerkin pmat
> -pc_use_amat false
>
> I just assumed that it’s a default behavior of the PC object.
>
> So to clarify my case, I don't use nonlinear multigrid. Galerkin is
> expected to deal with Pmat only, and it's enough if Amat implements a
> matrix-vector product for the Krylov accelerator.
>
> Matt, the reason for switching Amat during the iteration is a quite common
> Picard-Newton combination. Jacobian matrix gives accurate updates close to
> the solution, but is rather unstable far form the solution. Picard matrix
> (approximate Jacobian) is quite the opposite – it’s kind of stable, but
> slow. So the idea is to begin the iteration with Picard matrix, and switch
> to the Jacobian later.
>
> If the assembled matrices are used, then the standard SNES interface is
> just perfect. I can decide how to fill the matrices. But I don’t bother
> with  Jacobian assembly and want to use a built-in MFFD approximation
> instead. I did quite a few tests previously and figured out that MFFD is
> practically the same as closed-from matrix-free Jacobian for the later
> stages of the iteration. The Picard matrix still does a good job as a
> preconditioner. But it is important to start the iteration with Picard and
> only change to MFFD later.
>
> Is my workaround with the shell matrix acceptable, or there is a better
> solution?
>

Given what you write, it sounds like you already have a good heuristic for
when to switch from Picard to Newton,
Hence I think the simplest option is just to use two seperate SNES objects
- one for performing Picard and one for Newton.
The stopping condition for the Picard object would encode your heuristic to
abort earlier when the solution was deemed sufficiently accurate.

Thanks,
Dave


>
> Thanks,
> Anton
> On 13.06.21 20:52, Barry Smith wrote:
>
>
>   Anton,
>
>   -pc_mg_galerkin pmat
>
>   Though it seems simple, there is some subtly in swapping out matrices
> with SNES.
>
>   When using multigrid with SNES there are at least five distinct uses of
> the Jacobian operator.
>
>    - Perform matrix-vector product in line search to check Wolf
>       sufficient decrease convergence criteria
>       - Perform the matrix-vector product for the Krylov accelerator of
>       the system
>       - Perform smoothing on the finest level of MG
>       - Perform the matrix-vector product needed on the finest level of
>       MG to compute the residual that will be restricted to the coarser level of
>       multigrid
>       - When using Galerkin products to compute the coarser grid operator
>       performing the Galerkin matrix triple product
>
>
> when one swaps out the mat, which of these do they wish to change? The
> first two seem to naturally go together as do the last three. In your case
> I presume you want to swap for the first two, but always use pmat for the
> last three? To achieve this you will also need -pc_use_amat  false
>
> If you run with -info and -snes_view it will print out some of the
> information about which operator it is using for each case, but probably
> not all of them.
>
> Note: if the pmat is actually an accurate computation of the Jacobian then
> it is likely best not to ever use a matrix-free product. It is only when
> pmat is approximated in some specific way that using the matrix-free
> product would be useful to insure the "Newton" method actually computes a
> Newton step.
>
> Barry
>
>
>
> On Jun 13, 2021, at 11:21 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Sun, Jun 13, 2021 at 10:55 AM Anton Popov <popov at uni-mainz.de> wrote:
>
>> Hi,
>>
>> I want a simple(?) thing. I want to decide and be able to assign the
>> Jacobian matrix (Amat) on the fly within the FormJacobian function (i.e.
>> during Newton iteration) to one of the following options:
>>
>> 1) built-in MFFD approximation
>> 2) assembled preconditioner matrix (Pmat)
>>
>> I have not found this scenario demonstrated in any example, therefore
>> I’m asking how to do that.
>>
>> Currently I do the following:
>>
>> 1) setup Amat as a shell matrix with a MATOP_MULT operation that simply
>> retrieves a matrix object form its context and calls MatMult on it.
>>
>> 2) if I need MFFD, I put a matrix generated with MatCreateSNESMF in the
>> Amat context (of course I also call MatMFFDComputeJacobian before that).
>>
>> 3) if I need Pmat, I simply put Pmat in the Amat context.
>>
>> 4) call MatAssemblyBegin/End on Amat
>>
>> So far so good.
>>
>> However, shell Amat and assembled Pmat generate a problem if Galerkin
>> multigrid is requested as a preconditioner (I just test on 1 CPU):
>>
>> [0]PETSC ERROR: MatPtAP requires A, shell, to be compatible with P,
>> seqaij (Misses composed function MatPtAP_shell_seqaij_C)
>> [0]PETSC ERROR: #1 MatPtAP()
>> [0]PETSC ERROR: #2 MatGalerkin()
>> [0]PETSC ERROR: #3 PCSetUp_MG()
>> [0]PETSC ERROR: #4 PCSetUp()
>> [0]PETSC ERROR: #5 KSPSetUp()
>> [0]PETSC ERROR: #6 KSPSolve()
>> [0]PETSC ERROR: #7 SNESSolve_NEWTONLS()
>> [0]PETSC ERROR: #8 SNESSolve()
>>
>> It seems like PETSc tries to apply Galerkin coarsening to the shell Amat
>> matrix instead of the assembled Pmat. Why?
>>
>> Pmat is internally generated by SNES using a DMDA attached to SNES, so
>> it has everything to define Galerkin coarsening. And it actually works
>> if I just get rid of the shell Amat.
>>
>> I can get around this problem by wrapping a PC object in a shell matrix
>> and pass it as Pmat. This is a rather ugly approach, so I wonder how to
>> resolve the situation in a better way, if it is possible.
>>
>
> Hi Anton,
>
> You are correct that there is no specific test, so I can believe that a
> bug might be lurking here.
> I believe the way it is supposed to work is that you set the type of
> Galerkin coarsening that you
> want
>
>
> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCMGSetGalerkin.html
>
> So I am thinking you want 'pmat' only, and you would be in charge of
> making the coarse MFFD operator
> and telling PCMG about it. I could imagine that you might want us to
> automatically do that, but we would
> need some way to know that it is MFFD, and with the scheme above we do not
> have that.
>
> What is the advantage of switching representations during the Newton
> iteration?
>
>   Thanks,
>
>      Matt
>
>
>> Thanks.
>> Anton
>>
> --
> 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
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
>
>
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