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<p class="MsoNormal"><span style="font-family:"Courier New"">Dear all, <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""><o:p> </o:p></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. <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><o:p> </o:p></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">
http://www.mcs.anl.gov/petsc/petsc-current/src/ts/examples/tutorials/ex1f.F.html</a>.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><o:p> </o:p></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).
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><o:p> </o:p></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:
<br>
<br>
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>
<br>
Henrik<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><br>
<br>
<br>
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New";mso-fareast-language:DE">--
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New";mso-fareast-language:DE">Dipl.-Math. Henrik Büsing<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New";mso-fareast-language:DE">Institute for Applied Geophysics and Geothermal Energy<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New";mso-fareast-language:DE">E.ON Energy Research Center<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-family:"Courier New";mso-fareast-language:DE">RWTH Aachen University<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New";mso-fareast-language:DE">------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New";mso-fareast-language:DE">Mathieustr. 10 | Tel +49 (0)241 80 49907<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New";mso-fareast-language:DE">52074 Aachen, Germany | Fax +49 (0)241 80 49889<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New";mso-fareast-language:DE">------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New";mso-fareast-language:DE">http://www.eonerc.rwth-aachen.de/GGE<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New";mso-fareast-language:DE">hbuesing@eonerc.rwth-aachen.de<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Courier New";mso-fareast-language:DE">------------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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