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This is very helpful. JFNK + Qn in that paper sounds really promising.
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<div>Jed, is there a flag I can quickly try to recover some performance related to that paper (snes ex48.c)? Thanks.</div>
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<div>Qi</div>
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On May 3, 2022, at 7:27 AM, Matthew Knepley <knepley@gmail.com> wrote:<br>
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<div dir="ltr">On Tue, May 3, 2022 at 9:08 AM Tang, Qi <<a href="mailto:tangqi@msu.edu">tangqi@msu.edu</a>> wrote:<br>
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<div dir="auto">Pierre and Matt,
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<div>Thanks a lot for the suggestion. It looks like lag Jacobian is exactly what I need. We will try that.</div>
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<div>I always thought ngmres is a fancy version of Anderson. Is there any reference or example related to what you said in which one actually implemented an approximated Jacobian through ngmres? This sounds very interesting.</div>
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<div>Jed and Peter do it here:</div>
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<div>@inproceedings{brown2013quasinewton,<br>
author = {Jed Brown and Peter Brune},<br>
title = {Low-rank quasi-{N}ewton updates for robust {J}acobian lagging in {N}ewton-type methods},<br>
year = {2013},<br>
booktitle = {International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering},<br>
pages = {2554--2565},<br>
petsc_uses={KSP},<br>
}<br>
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<div> Thanks,</div>
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<div>Qi<br>
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On May 3, 2022, at 4:51 AM, Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> wrote:<br>
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<div dir="ltr">On Tue, May 3, 2022 at 2:58 AM Pierre Seize <<a href="mailto:pierre.seize@onera.fr" target="_blank">pierre.seize@onera.fr</a>> wrote:<br>
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Hi,<br>
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If I may, is this what you want ?<br>
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<a href="https://urldefense.com/v3/__https://petsc.org/main/docs/manualpages/SNES/SNESSetLagJacobian.html__;!!HXCxUKc!zIB-QYseFS9GsRBrb4wzwezVTB9DKqY_PBYGWYql4tLtLTBwX552ukXeZk_z0ZASYNl5x6QlBwDt6Q$" rel="noreferrer" target="_blank">https://petsc.org/main/docs/manualpages/SNES/SNESSetLagJacobian.html</a></blockquote>
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<div>Yes, this is a good suggestion.</div>
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<div>Also, you could implement an approximation to the Jacobian.</div>
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<div>You could then improve it at each iteration using a secant update. This is what the Generalized Broyden methods do. We call them NGMRES.</div>
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<div> Thanks,</div>
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Pierre<br>
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On 03/05/2022 06:21, Tang, Qi wrote:<br>
> Hi,<br>
> Our code uses FDcoloring to compute Jacobian. The log file indicates most of time is spent in evaluating residual (2600 times in one Newton solve) while it only needs 3 nonlinear iterations and 6 total linear iterations thanks to the fieldsplit pc.<br>
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> As a temporary solution, is it possible to evaluate Jacobian only once in one Newton solve? This should work well based on my other experience if pc is very efficient. But I cannot find such a flag.<br>
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> Is there any other solution, other than implementing the analytical Jacobian?<br>
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> Thanks,<br>
> Qi<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>
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