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?
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 <[email protected]
<mailto:[email protected]>> wrote:
On Sun, Jun 13, 2021 at 10:55 AM Anton Popov <[email protected]
<mailto:[email protected]>> 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/>
