<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Thu, Aug 24, 2017 at 2:29 AM, Klaij, Christiaan <span dir="ltr"><<a href="mailto:C.Klaij@marin.nl" target="_blank">C.Klaij@marin.nl</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>Matt,<br>
<br>
Thanks, I can understand the lower condition number of P A, but<br>
what about r? Doesn't that change to P r and if so why can we<br>
assume that ||r|| and ||P r|| have the same order?<br></p></div></blockquote><div>r and Pr are the things we can control. We make them whatever we want.</div><div><br></div><div> Matt <br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr" style="font-size:12pt;color:#000000;background-color:#ffffff;font-family:Calibri,Arial,Helvetica,sans-serif"><p>
Chris<br>
<br>
</p>
<div style="color:rgb(33,33,33)"></div>
<br>
<font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold">dr. ir.</font><font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold">
</font><font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold">Christiaan</font><font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold">
</font><font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold">Klaij</font><font size="3" face="Segoe UI"></font><font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold"> |
</font><font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold">Senior Researcher</font><font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold"> |
</font><font style="font-family:Verdana;font-size:8pt;color:#7d7d7d;font-weight:bold">Research & Development</font><br>
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<hr style="display:inline-block;width:98%">
<div id="m_844515160451864277divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" color="#000000" face="Calibri, sans-serif"><b>From:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Sent:</b> Wednesday, August 23, 2017 8:37 AM<br>
<b>To:</b> Barry Smith<br>
<b>Cc:</b> Klaij, Christiaan; <a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a><br>
<b>Subject:</b> Re: [petsc-users] Petsc ILU PC Change between 3.6.4 and 3.7.x?</font>
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<div class="gmail_quote">On Wed, Aug 23, 2017 at 2:30 AM, Barry Smith <span dir="ltr">
<<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
Some argue that the preconditioned residual is "closer to" the norm of the error than the unpreconditioned norm. I don't have a solid mathematical reason to prefer left preconditioning with the preconditioned norm.</blockquote>
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<div>Because you have || x - x_exact || < k(A) || r ||</div>
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</div>
<div>where r is the residual and k is the condition number of A. If instead of A you use P A, which we assume has a lower condition number, then</div>
<div>this bound is improved.</div>
<div><br>
</div>
<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">
<span class="m_844515160451864277HOEnZb"><font color="#888888"><br>
Barry<br>
</font></span>
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<div class="m_844515160451864277h5"><br>
<br>
<br>
> On Aug 22, 2017, at 11:27 PM, Klaij, Christiaan <<a href="mailto:C.Klaij@marin.nl" target="_blank">C.Klaij@marin.nl</a>> wrote:<br>
><br>
> Barry,<br>
><br>
> Thanks for the explanation.<br>
><br>
> We do have some rare cases that give false convergence, but<br>
> decided to use<br>
><br>
> CALL KSPSetNormType(ksp,KSP_NORM_UN<wbr>PRECONDITIONED,ierr)<br>
><br>
> so that convergence is always based on the true residual. Our<br>
> results are much more consistent now. So that could have been<br>
> your protection against the rare case as well, right? Why do you<br>
> prefer left preconditioning?<br>
><br>
> Chris<br>
><br>
><br>
><br>
> dr. ir. Christiaan Klaij | Senior Researcher | Research & Development<br>
> MARIN | T <a href="tel:%2B31%20317%2049%2033%2044" value="+31317493344" target="_blank">+31 317 49 33 44</a> | mailto:<a href="mailto:C.Klaij@marin.nl" target="_blank">C.Klaij@marin.nl</a> |
<a href="http://www.marin.nl" rel="noreferrer" target="_blank">http://www.marin.nl</a><br>
><br>
> MARIN news: <a href="http://www.marin.nl/web/News/News-items/BlueWeek-October-911-Rostock.htm" rel="noreferrer" target="_blank">
http://www.marin.nl/web/News/N<wbr>ews-items/BlueWeek-October-911<wbr>-Rostock.htm</a><br>
><br>
> ______________________________<wbr>__________<br>
> From: Barry Smith <<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>><br>
> Sent: Tuesday, August 22, 2017 6:25 PM<br>
> To: Klaij, Christiaan<br>
> Cc: <a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a><br>
> Subject: Re: [petsc-users] Petsc ILU PC Change between 3.6.4 and 3.7.x?<br>
><br>
>> On Aug 22, 2017, at 6:49 AM, Klaij, Christiaan <<a href="mailto:C.Klaij@marin.nl" target="_blank">C.Klaij@marin.nl</a>> wrote:<br>
>><br>
>> We also faced this problem in our code. So I've added:<br>
>><br>
>> CALL PetscOptionsSetValue(PETSC_NUL<wbr>L_OBJECT,"-sub_pc_factor_shift<wbr>_type","nonzero",ierr)<br>
>><br>
>> since there seems to be no setter function for this (correct me<br>
>> if I'm wrong). Then everythings fine again.<br>
>><br>
>> Out of curiosity, what was the reason to change the default<br>
>> behaviour?<br>
><br>
> The reason we changed this is that we would rather have a failure that makes the user aware of a serious problem then to produce "garbage" results. In some rare cases the shift can cause a huge jump in the preconditioned residual which then decreases rapidly
while the true residual does not improve. This results in the KSP thinking it has converged while in fact it has essentially garbage for an answer. Under the previous model, where we shifted by default, users would in this rare case think they had reasonable
solutions when they did not.<br>
><br>
> For many users, such as yourself, the previous default behavior was fine because you didn't have the "rare case" but we decided it was best to protect against the rare case even though it would require other users such as yourself to add the option.<br>
><br>
> Barry<br>
<br><span class="HOEnZb"><font color="#888888">
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-- <br>
<div class="m_844515160451864277gmail_signature">
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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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<div><a href="http://www.caam.rice.edu/~mk51/" target="_blank">http://www.caam.rice.edu/~<wbr>mk51/</a><br>
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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>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">http://www.caam.rice.edu/~mk51/</a><br></div></div></div>
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