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</div><div class="ydpa597b1fyahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px;" dir="ltr" data-setdir="false">Thanks Matthew and Mark!</div><div class="ydpa597b1fyahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px;" dir="ltr" data-setdir="false"><br></div><div class="ydpa597b1fyahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px;" dir="ltr" data-setdir="false">Qin</div><div class="ydpa597b1fyahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px;"><br></div><div class="ydpa597b1fyahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px;">
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On Friday, June 12, 2020, 12:22:08 PM CDT, Mark Adams <mfadams@lbl.gov> wrote:
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<div><div id="ydp2721000fyiv1984912742"><div><div dir="ltr"><div dir="ltr"><br clear="none"></div><br clear="none"><div class="ydp2721000fyiv1984912742gmail_quote"><div class="ydp2721000fyiv1984912742gmail_attr" dir="ltr">On Fri, Jun 12, 2020 at 12:56 PM Qin Lu via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank" rel="nofollow" shape="rect">petsc-users@mcs.anl.gov</a>> wrote:<br clear="none"></div><blockquote class="ydp2721000fyiv1984912742gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex;"><div><div style="font-family:Helvetica, Arial, sans-serif;font-size:13px;"><div dir="ltr">Hello,</div><div dir="ltr"><br clear="none"></div><div dir="ltr">I plan to solve a small sparse linear equation system using the direct solver, since the number of unknowns is small (less than 1000). Here I got a few questions:</div><div dir="ltr"><br clear="none"></div><div dir="ltr">1. Is there a general guide line on the size of the system that direct solver is more efficient than iterative solver?</div></div></div></blockquote><div><br clear="none"></div><div>No. Direct solvers are about O(N^2) complexity and iteratives solvers can be O(N) - O(N^inf)</div><div> </div><blockquote class="ydp2721000fyiv1984912742gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex;"><div><div style="font-family:Helvetica, Arial, sans-serif;font-size:13px;"><div dir="ltr">2. Is the native Petsc direct solver (using KSPPREONLY and PCLU) designed to solve dense system or sparse system?</div></div></div></blockquote><div><br clear="none"></div><div>sparse.</div><div> </div><blockquote class="ydp2721000fyiv1984912742gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex;"><div><div style="font-family:Helvetica, Arial, sans-serif;font-size:13px;"><div dir="ltr">3. Is the native Petsc direct solver comparable to SuperLU and MUMPS in performance? Do they use different algorithms?</div></div></div></blockquote><div><br clear="none"></div><div>PETSc's is only in serial and CPU. MUMPS and SuperLU are MPI parallel. SuperLU runs on GPUs.</div><div><br clear="none"></div><div>SuperLU and MUMPS have more optimizations, such that there is probably a significant difference on some problems but it's hard to say in general. </div><div class="ydp2721000fyiv1984912742yqt6122559558" id="ydp2721000fyiv1984912742yqtfd76872"><div> </div><blockquote class="ydp2721000fyiv1984912742gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex;"><div><div style="font-family:Helvetica, Arial, sans-serif;font-size:13px;"><div dir="ltr"><br clear="none"></div><div dir="ltr">Thanks in advance for your help.</div><div dir="ltr"><br clear="none"></div><div dir="ltr">Best Regards,</div><div dir="ltr">Qin</div></div></div></blockquote></div></div></div></div></div></div>
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