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<p class="MsoNormal"><span lang="EN-GB" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Thank you Matt. I’ll try that soon. Will let you know if this works for me.<o:p></o:p></span></p>
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<p class="MsoNormal"><b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> Matthew Knepley [mailto:knepley@gmail.com]
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<b>Sent:</b> donderdag 1 mei 2014 0:09<br>
<b>To:</b> Danny Lathouwers - TNW<br>
<b>Cc:</b> petsc-users@mcs.anl.gov<br>
<b>Subject:</b> Re: [petsc-users] singular matrix solve using MAT_SHIFT_POSITIVE_DEFINITE option<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">On Wed, Apr 30, 2014 at 2:53 PM, Danny Lathouwers - TNW <<a href="mailto:D.Lathouwers@tudelft.nl" target="_blank">D.Lathouwers@tudelft.nl</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Dear users,<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">I encountered a strange problem. I have a singular matrix P (Poisson, Neumann boundary conditions, N=4). The rhs b sums to 0.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">If I hand-fill the matrix with the right entries (non-zeroes only) things work with KSPCG and ICC preconditioning and using the MAT_SHIFT_POSITIVE_DEFINITE option.
Convergence in 2 iterations to (a) correct solution. So far for the debugging problem.</span><o:p></o:p></p>
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<p class="MsoNormal">That option changes the preconditioner matrix to (alpha I + P). I don't know of a theoretical reason that this<o:p></o:p></p>
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<p class="MsoNormal">should be a good preconditioner, but perhaps it exists. Certainly ICC is exquisitely sensitive (you can easily<o:p></o:p></p>
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<p class="MsoNormal">write down matrices where an epsilon change destroys convergence).<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Yes, you should use null space, and here it is really easy<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> -ksp_constant_null_space<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Its possible that this fixes your convergence, if the ICC perturbation was introducing components in the<o:p></o:p></p>
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<p class="MsoNormal">null space to your solution.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> Matt<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">My real problem computes P from D * M * D^T. If I do this I get the same matrix (on std out I do not see the difference to all digits).</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">The system P * x = b now does NOT converge.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">More strange is that is if I remove the zeroes from D then things do work again.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">Either things are overly sensitive or I am misusing petsc.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">It does work when using e.g. the AMG preconditioner (again it is a correct but different solution). So system really seems OK.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">Should I also use the Null space commands as I have seen in some of the examples as well?</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">But, I recall from many years ago when using MICCG (alpha) preconditioning that no such tricks were needed for CG with Poisson-Neumann. I am supposing the MAT_SHIFT_POSITIVE_DEFINITE
option does something similar as MICCG.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">For clarity I have included the code (unfortunately this is the smallest I could get it; it’s quite straightforward though).</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">By setting the value of option to 1 in main.f90 the code use P = D * M * D^T otherwise it will use the hand-filled matrix.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">The code prints the matrix P and solution etc.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">Anyone any hints on this?</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">What other preconditioners (serial) are suitable for this problem besides ICC/AMG?</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB">Thanks very much.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="color:#888888">Danny Lathouwers</span><span style="color:#888888"><o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-GB" style="color:#888888"> </span><span style="color:#888888"><o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">-- <br>
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 <o:p></o:p></p>
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