<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div></div><div><br></div><div><br>On Jun 22, 2018, at 4:49 PM, Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:<br><br></div><blockquote type="cite"><div><div dir="ltr"><div class="gmail_quote"><div dir="ltr">On Fri, Jun 22, 2018 at 1:47 PM Boyce Griffith <<a href="mailto:griffith@cims.nyu.edu">griffith@cims.nyu.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto"><div></div><div>Can you set up the preconditioner so that you can just use GMRES?</div></div></blockquote><div><br></div><div>So I think what Boyce is saying is, can't you fix the number of iterates in the inner Krylov solvers so that it becomes a linear</div><div>operator and you can use GMRES?</div></div></div></div></blockquote><div><br></div>Yes that is it.<div><br></div><div>I think we default to FGMRES for robustness, because the preconditioner can easily be configured to be nonlinear, but unless you have made some big changes to the algorithm that I think you are using, I think it should be possible to set it up as a stationary linear operator.</div><div><br></div><div><blockquote type="cite"><div><div dir="ltr"><div class="gmail_quote"><div> Thanks,</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 dir="auto"><div>On Jun 22, 2018, at 4:33 PM, Nishant Nangia <<a href="mailto:nishantnangia329@gmail.com" target="_blank">nishantnangia329@gmail.com</a>> wrote:<br><br></div><blockquote type="cite"><div><div dir="ltr">Hi,<div><br></div><div>I am solving a saddle point system using a shell preconditioner (which itself uses Krylov solvers, hence the use of FGMRES). I had added the option to re-scale parts of the saddle point system to minimize loss of floating point precision for cases where there are varying orders of magnitude in the system/unknowns.</div><div><br></div><div>I wanted to show that re-scaling can alleviate large differences between the preconditioned and unpreconditioned residual norms. However, I notice that FGMRES only supports right preconditioning, meaning the preconditioned residual is never formed/used (I think).</div><div><br></div><div>Is there any way to form the preconditioned norm for FGMRES, or does it just not make sense in the context of right-preconditioned iterative solvers? Is there any way to show that the re-scaling is improving the solver convergence (i.e. showing that it ensures that the true and relative residual are close to each other)?<br clear="all"><div><div class="m_-6010472951141135462gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><br><b>Nishant Nangia</b><div>Northwestern University<br><div>Ph.D. Candidate | Engineering Sciences and Applied Mathematics<br></div></div><div><span style="font-family:arial;font-size:small">Tech L386</span><br></div></div></div></div></div></div>
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</div></blockquote></div></blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" 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></div>
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