<div dir="ltr"><div dir="ltr">On Mon, Feb 17, 2020 at 8:56 AM Yuyun Yang <<a href="mailto:yyang85@stanford.edu">yyang85@stanford.edu</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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Hello,</div>
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I actually have a question about the usage of DMDA since I'm quite new to this. <span style="font-family:Calibri,Arial,Helvetica,sans-serif;background-color:rgb(255,255,255);display:inline">I wonder if the DMDA
suite of functions can be directly called on vectors created from VecCreate? Or the vectors have to be formed by DMDACreateGlobalVector?</span></div></div></blockquote><div><br></div><div>Most things work the same. About the only thing that is different is that we set a special viewer for vectors from DMDACreateGlobalVector()</div><div>which puts it in lexicographic order on output.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"><span style="font-family:Calibri,Arial,Helvetica,sans-serif;background-color:rgb(255,255,255);display:inline"> I'm also not sure about what the dof and stencil width arguments do.</span></div></div></blockquote><div><br></div><div>'dof' is how many unknowns lie at each vertex. 'sw' is the width of the ghost region for local vectors.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">
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I'm still unsure about the usage of MatCreateShell and MatShellSetOperation, since it seems that MyMatMult should still have 3 inputs just like MatMult (the matrix and two vectors).</div></div></blockquote><div><br></div><div>MatShell is a type where you provide your own function implementations, rather than using those for a particular storage format, like AIJ.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)"> Since I'm not forming the matrix, does that mean the matrix input is meaningless
but still needs to exist for the sake of this format?</div></div></blockquote><div><br></div><div>It means you calculate the output yourself, using the input.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">
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After I create such a shell matrix, can I use it like a regular matrix in KSP and utilize preconditioners?</div></div></blockquote><div><br></div><div>Many preconditioners want access to individual elements of the matrix, which usually will not work with shell matrices, since the</div><div>user just wants to provide the multiply routine.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">
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Thanks!</div>
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Yuyun</div>
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<div id="gmail-m_456101638831796992divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> petsc-users <<a href="mailto:petsc-users-bounces@mcs.anl.gov" target="_blank">petsc-users-bounces@mcs.anl.gov</a>> on behalf of Yuyun Yang <<a href="mailto:yyang85@stanford.edu" target="_blank">yyang85@stanford.edu</a>><br>
<b>Sent:</b> Sunday, February 16, 2020 3:12 AM<br>
<b>To:</b> Smith, Barry F. <<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>><br>
<b>Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:</b> Re: [petsc-users] Matrix-free method in PETSc</font>
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Thank you, that is very helpful information indeed! I will try it and send you my code when it works.</div>
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Best regards,</div>
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Yuyun</div>
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<div id="gmail-m_456101638831796992x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Smith, Barry F. <<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>><br>
<b>Sent:</b> Saturday, February 15, 2020 10:02 PM<br>
<b>To:</b> Yuyun Yang <<a href="mailto:yyang85@stanford.edu" target="_blank">yyang85@stanford.edu</a>><br>
<b>Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:</b> Re: [petsc-users] Matrix-free method in PETSc</font>
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<div> Yuyun,<br>
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If you are speaking about using a finite difference stencil on a structured grid where you provide the Jacobian vector products yourself by looping over the grid doing the stencil operation we unfortunately do not have exactly that kind of example.
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But it is actually not difficult. I suggest starting with src/ts/examples/tests/ex22.c It computes the sparse matrix explicitly with FormIJacobian()
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What you need to do is instead in main() use MatCreateShell() and MatShellSetOperation(,MATOP_MULT,(void (*)(void))MyMatMult) then provide the routine MyMatMult() to do your stencil based matrix free product; note that you can create this new routine by
taking the structure of IFunction() and reorganizing it to do the Jacobian product instead. You will need to get the information about the shell matrix size on each process by calling DMDAGetCorners().
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You will then remove the explicit computation of the Jacobian, and also remove the Event stuff since you don't need it.<br>
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Extending to 2 and 3d is straight forward. <br>
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Any questions let us know.<br>
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Barry<br>
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If you like this would make a great merge request with your code to improve our examples.<br>
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> On Feb 15, 2020, at 9:42 PM, Yuyun Yang <<a href="mailto:yyang85@stanford.edu" target="_blank">yyang85@stanford.edu</a>> wrote:<br>
> <br>
> Hello team,<br>
> <br>
> I wanted to apply the Krylov subspace method to a matrix-free implementation of a stencil, such that the iterative method acts on the operation without ever constructing the matrix explicitly (for example, when doing backward Euler).<br>
> <br>
> I'm not sure whether there is already an example for that somewhere. If so, could you point me to a relevant example?<br>
> <br>
> Thank you!<br>
> <br>
> Best regards,<br>
> Yuyun<br>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><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.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>