<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Tue, Nov 7, 2017 at 4:19 AM, Buesing, Henrik <span dir="ltr"><<a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<p class="MsoNormal"><span style="font-family:"Courier New"">Dear all, <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><u></u> <u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">I am solving a system of nonlinear, transient PDEs. I am using Newton’s method in every time step to solve the nonlinear algebraic equations. Of course, Newton’s method only converges
if the initial guess is sufficiently close to the solution. <br>
<br>
This is often not the case and Newton’s method diverges. Then, I reduce the time step and try again. This can become prohibitively costly, if the time steps get very small. I am thus looking for variants of Newton’s method, which have a bigger convergence radius
or ideally converge all the time. <u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><u></u> <u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">I tried out the pseudo-timestepping described in
<a href="http://www.mcs.anl.gov/petsc/petsc-current/src/ts/examples/tutorials/ex1f.F.html" target="_blank">
http://www.mcs.anl.gov/petsc/<wbr>petsc-current/src/ts/examples/<wbr>tutorials/ex1f.F.html</a>.
<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><u></u> <u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">However, this does converge even worse. I am seeing breakdown when I have phase changes (e.g. liquid to two-phase).
<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><u></u> <u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">I was under the impression that pseudo-timestepping should converge better. Thus, my question:
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Am I doing something wrong or is it possible that Newton’s method converges and pseudo-timestepping does not?<br>
<br>
Thank you for any insight on this. <br></span></p></div></div></blockquote><div><br></div><div>Hi Hendrik,</div><div><br></div><div>I would try using NGMRES as a nonlinear preconditioner. I have an example in my tutorial slides for using it with SNES ex19.</div><div>I hope this will work because I suspect that around the phase boundary Newton directions are noisy, since sometimes you</div><div>step into the other phase. NGMRES takes a few directions (you set the m) and then picks the best one.</div><div><br></div><div> Hopefully this helps,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div lang="DE" link="#0563C1" vlink="#954F72"><div class="m_-5508726634193856442WordSection1"><p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">
Henrik<u></u><u></u></span></p>
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<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><u></u> <u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">--
<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">Dipl.-Math. Henrik Büsing<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">Institute for Applied Geophysics and Geothermal Energy<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">E.ON Energy Research Center<u></u><u></u></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New"">RWTH Aachen University<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-family:"Courier New""><a href="mailto:hbuesing@eonerc.rwth-aachen.de" target="_blank">hbuesing@eonerc.rwth-aachen.de</a><u></u><u></u></span></p>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><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.caam.rice.edu/~mk51/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div>
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