<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><br class="webkit-block-placeholder"></div> We need to come up with a good general PETSc infrastructure for solving these types of systems,<div>that supports a variety of solving approaches.<br><div><br class="webkit-block-placeholder"></div><div> Barry</div><div><br class="webkit-block-placeholder"></div><div><br><div><div>On Jan 10, 2008, at 10:36 AM, filippo wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div lang="IT" link="blue" vlink="purple"><o:smarttagtype namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="City"><o:smarttagtype namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="place"><o:smarttagtype namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="metricconverter"><div class="Section1"><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">Dear Professor Barry,<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">I'm a PHD student at University of<span class="Apple-converted-space"> </span><st1:place w:st="on"><st1:city w:st="on">Rome</st1:city></st1:place><span class="Apple-converted-space"> </span>'La Sapienza' and I'm developing a<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">fluid dynamic Finite Element code in a LINUX environment.<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "> <o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">After reading the book you have published, we decided to use PETSC and we<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">downloaded all the package from the web site.<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "> <o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">To resolve the Navier-Stokes system I have to resolve the following linear equation<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">system<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" color="black" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; color: black; "><o:p> </o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="4" color="black" face="Courier New"><span lang="EN-GB" style="font-size: 14pt; color: black; ">|A B| |u| |f|<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="4" color="black" face="Courier New"><span lang="EN-GB" style="font-size: 14pt; color: black; ">| | | | = | |<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="4" color="black" face="Courier New"><span lang="EN-GB" style="font-size: 14pt; color: black; ">|B<sup>T </sup>0| |p| |g|<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "><o:p> </o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">I want to solve the previous system with the pressure Shur complement technique.<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "><o:p> </o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">Given an initial guess for pressure p I would like to solve the following system<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "><o:p> </o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "> </span></font><font size="4"><span lang="EN-GB" style="font-size: 14pt; ">(BA<sup>-1</sup>B<sup>T</sup>)*p=BA<sup>-1</sup>f-g<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="4" face="Courier New"><span lang="EN-GB" style="font-size: 14pt; "><o:p> </o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">Then I calculate the variable u:<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "><o:p> </o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "> </span></font><font size="4"><span lang="EN-GB" style="font-size: 14pt; ">u=A<sup>-1</sup>(f-B<sup>T</sup>p)<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="4" face="Courier New"><span lang="EN-GB" style="font-size: 14pt; "><o:p> </o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">I’m wondering if it is possible, with PETSC, to solve the shur complement<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">equation system without allocating and calculating the global matrix<span class="Apple-converted-space"> </span></span></font><font size="4"><span lang="EN-GB" style="font-size: 14pt; ">(BA<sup>-1</sup>B<sup>T</sup>)<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">i.e. if it is possible to give to PETSC the single matrix<span class="Apple-converted-space"> </span></span></font><font size="4"><span lang="EN-GB" style="font-size: 14pt; ">B</span></font><span lang="EN-GB"><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span></span><font size="4"><span lang="EN-GB" style="font-size: 14pt; ">A<sup>-<st1:metricconverter productid="1 in" w:st="on">1<font size="2"><span style="font-size: 10pt; vertical-align: baseline; "><span class="Apple-converted-space"> </span>in</span></font></st1:metricconverter><font size="2"><span style="font-size: 10pt; vertical-align: baseline; "><span class="Apple-converted-space"> </span>order to save allocating memory.<o:p></o:p></span></font></sup></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "> <o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">Please could you give me any suggestions in order to solve this problem with PETSC ?<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">Please in case it is possible, could you give some examples showing the solution of the problem ?<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "> <o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">Thanks in advance for your time replay.<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; "> <o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 10pt; font-family: 'Courier New'; "><font size="2" face="Courier New"><span lang="EN-GB" style="font-size: 10pt; ">Filippo Menichini<o:p></o:p></span></font></div><div style="margin-top: 0cm; margin-right: 0cm; margin-left: 0cm; margin-bottom: 0.0001pt; font-size: 12pt; font-family: 'Times New Roman'; "><font size="2" face="Arial"><span lang="EN-GB" style="font-size: 10pt; font-family: Arial; "><o:p> </o:p></span></font></div></div><br><p><font size="2">No virus found in this outgoing message.<br>Checked by AVG Free Edition.<br>Version: 7.5.516 / Virus Database: 269.19.0/1216 - Release Date: 09/01/2008 10.16<br></font></p></o:smarttagtype></o:smarttagtype></o:smarttagtype></div></span></blockquote></div><br></div></div></body></html>