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<div class="moz-cite-prefix">On 14.06.21 15:04, Dave May wrote:<br>
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<div>Hi Anton,<br>
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Hi Dave,<br>
<blockquote type="cite"
cite="mid:CAJ98EDr=14Qzq-c8e3-XnZf87L+JnDK6N12HAtrHBhz4ubeAAw@mail.gmail.com">
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<div dir="ltr" class="gmail_attr">On Mon, 14 Jun 2021 at
14:47, Anton Popov <<a href="mailto:popov@uni-mainz.de"
moz-do-not-send="true">popov@uni-mainz.de</a>> wrote:<br>
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<p>Hi Barry & Matt,<br>
<br>
thanks for your quick response. These options were
exactly what I needed and expected:<br>
<br>
-pc_mg_galerkin pmat<br>
-pc_use_amat false<br>
<br>
I just assumed that it’s a default behavior of the PC
object.<br>
<br>
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.<br>
<br>
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.<br>
<br>
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.<br>
<br>
Is my workaround with the shell matrix acceptable, or
there is a better solution? <br>
</p>
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<div>Given what you write, it sounds like you already have a
good heuristic for when to switch from Picard to Newton,<br>
</div>
<div>Hence I think the simplest option is just to use two
seperate SNES objects - one for performing Picard and one
for Newton.<br>
</div>
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<p><br>
</p>
<p>Yes, I considered this option initially. Sometimes it is
necessary to switch back and forth between the methods, so it
becomes a bit messy to organize this in the code.</p>
<p>But maybe if Newton fails after Picard, I should just reduce the
time step and restart, instead of switching back to Picard.
Thanks, Dave.</p>
<p>Thanks,</p>
<p>Anton<br>
</p>
<p><br>
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<blockquote type="cite"
cite="mid:CAJ98EDr=14Qzq-c8e3-XnZf87L+JnDK6N12HAtrHBhz4ubeAAw@mail.gmail.com">
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<div>The stopping condition for the Picard object would encode
your heuristic to abort earlier when the solution was deemed
sufficiently accurate.<br>
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<div><br>
</div>
<div>Thanks,</div>
<div>Dave<br>
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<p> <br>
Thanks,<br>
Anton <br>
</p>
<div>On 13.06.21 20:52, Barry Smith wrote:<br>
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<div><br>
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<div> Anton,</div>
<div><br>
</div>
-pc_mg_galerkin pmat
<div><br>
</div>
<div> Though it seems simple, there is some subtly in
swapping out matrices with SNES.</div>
<div><br>
</div>
<div> When using multigrid with SNES there are at least
five distinct uses of the Jacobian operator. </div>
<div>
<ol>
<ul>
<li>Perform matrix-vector product in line search
to check Wolf sufficient decrease convergence
criteria</li>
<li>Perform the matrix-vector product for the
Krylov accelerator of the system</li>
<li>Perform smoothing on the finest level of MG</li>
<li>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</li>
<li>When using Galerkin products to compute the
coarser grid operator performing the Galerkin
matrix triple product</li>
</ul>
</ol>
<div><br>
</div>
<div>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</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>Barry</div>
<div><br>
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<div><br>
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<div>On Jun 13, 2021, at 11:21 AM, Matthew Knepley
<<a href="mailto:knepley@gmail.com"
target="_blank" moz-do-not-send="true">knepley@gmail.com</a>>
wrote:</div>
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<div dir="ltr">On Sun, Jun 13, 2021 at 10:55
AM Anton Popov <<a
href="mailto:popov@uni-mainz.de"
target="_blank" moz-do-not-send="true">popov@uni-mainz.de</a>>
wrote:<br>
</div>
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<blockquote class="gmail_quote"
style="margin:0px 0px 0px
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rgb(204,204,204);padding-left:1ex">Hi,<br>
<br>
I want a simple(?) thing. I want to decide
and be able to assign the <br>
Jacobian matrix (Amat) on the fly within
the FormJacobian function (i.e. <br>
during Newton iteration) to one of the
following options:<br>
<br>
1) built-in MFFD approximation<br>
2) assembled preconditioner matrix (Pmat)<br>
<br>
I have not found this scenario
demonstrated in any example, therefore <br>
I’m asking how to do that.<br>
<br>
Currently I do the following:<br>
<br>
1) setup Amat as a shell matrix with a
MATOP_MULT operation that simply <br>
retrieves a matrix object form its context
and calls MatMult on it.<br>
<br>
2) if I need MFFD, I put a matrix
generated with MatCreateSNESMF in the <br>
Amat context (of course I also call
MatMFFDComputeJacobian before that).<br>
<br>
3) if I need Pmat, I simply put Pmat in
the Amat context.<br>
<br>
4) call MatAssemblyBegin/End on Amat<br>
<br>
So far so good.<br>
<br>
However, shell Amat and assembled Pmat
generate a problem if Galerkin <br>
multigrid is requested as a preconditioner
(I just test on 1 CPU):<br>
<br>
[0]PETSC ERROR: MatPtAP requires A, shell,
to be compatible with P, <br>
seqaij (Misses composed function
MatPtAP_shell_seqaij_C)<br>
[0]PETSC ERROR: #1 MatPtAP()<br>
[0]PETSC ERROR: #2 MatGalerkin()<br>
[0]PETSC ERROR: #3 PCSetUp_MG()<br>
[0]PETSC ERROR: #4 PCSetUp()<br>
[0]PETSC ERROR: #5 KSPSetUp()<br>
[0]PETSC ERROR: #6 KSPSolve()<br>
[0]PETSC ERROR: #7 SNESSolve_NEWTONLS()<br>
[0]PETSC ERROR: #8 SNESSolve()<br>
<br>
It seems like PETSc tries to apply
Galerkin coarsening to the shell Amat <br>
matrix instead of the assembled Pmat. Why?<br>
<br>
Pmat is internally generated by SNES using
a DMDA attached to SNES, so <br>
it has everything to define Galerkin
coarsening. And it actually works <br>
if I just get rid of the shell Amat.<br>
<br>
I can get around this problem by wrapping
a PC object in a shell matrix <br>
and pass it as Pmat. This is a rather ugly
approach, so I wonder how to <br>
resolve the situation in a better way, if
it is possible.<br>
</blockquote>
<div><br>
</div>
<div>Hi Anton,</div>
<div><br>
</div>
<div>You are correct that there is no
specific test, so I can believe that a bug
might be lurking here.</div>
<div>I believe the way it is supposed to
work is that you set the type of Galerkin
coarsening that you</div>
<div>want</div>
<div><br>
</div>
<div> <a
href="https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCMGSetGalerkin.html"
target="_blank" moz-do-not-send="true">https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCMGSetGalerkin.html</a></div>
<div><br>
</div>
<div>So I am thinking you want 'pmat' only,
and you would be in charge of making the
coarse MFFD operator</div>
<div>and telling PCMG about it. I could
imagine that you might want us to
automatically do that, but we would</div>
<div>need some way to know that it is MFFD,
and with the scheme above we do not have
that.</div>
<div><br>
</div>
<div>What is the advantage of switching
representations during the Newton
iteration?</div>
<div><br>
</div>
<div> Thanks,</div>
<div><br>
</div>
<div> Matt</div>
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Thanks.<br>
Anton<br>
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-- <br>
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<div>What most experimenters take
for granted before they begin
their experiments is infinitely
more interesting than any
results to which their
experiments lead.<br>
-- Norbert Wiener</div>
<div><br>
</div>
<div><a
href="http://www.cse.buffalo.edu/~knepley/"
target="_blank"
moz-do-not-send="true">https://www.cse.buffalo.edu/~knepley/</a><br>
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