<div dir="ltr"><div dir="ltr">On Sun, Sep 10, 2023 at 4:16 PM Karthikeyan Chockalingam - STFC UKRI <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk">karthikeyan.chockalingam@stfc.ac.uk</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"><div class="msg3275008586399625363">
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<p class="MsoNormal"><span style="font-size:11pt">Thank you. I almost got it and have a couple of questions.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Let me summarize, I have an element Jacobian matrix of size 8 x 8 for QAUD4 (for variables u and v) ordered such that
</span><span style="font-size:11pt">the degrees of freedom at a node are grouped together i.e. [u1 v1 u2 v2 u3 v3 u4 v4].<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Q1) But this ordering of element
</span><span style="font-size:11pt">Jacobian matrix of size 8 x 8, does not have an on-diagonal and off-diagonal block structure? Does it not matter?</span></p></div></div></div></blockquote><div><br></div><div>It does have block structure in that each entry in your original matrix is now a 2x2 block entry in the matrix for 2 fields. </div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="msg3275008586399625363"><div lang="EN-GB" style="overflow-wrap: break-word;"><div class="m_3275008586399625363WordSection1"><p class="MsoNormal"></p>
<p class="MsoNormal"><span style="font-size:11pt">When assembling the element Jacobian into the system matrix A, I would make use of MatSetValues. For each element, I
<b>presume</b> m = 8 and n = 8 along with idxm and idxn, are passed to MatSetValues. Meaning I have to figure out the global index (say idxm) set of size 8 corresponding to the system matrix A.</span></p></div></div></div></blockquote><div><br></div><div>What you can do is call</div><div><br></div><div> <a href="https://petsc.org/main/manualpages/Mat/MatSetValuesBlocked/">https://petsc.org/main/manualpages/Mat/MatSetValuesBlocked/</a></div><div><br></div><div>and give the same indices that you would have given for the original matrix, but instead of a value at each location, we now have a 2x2 block.</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 class="msg3275008586399625363"><div lang="EN-GB" style="overflow-wrap: break-word;"><div class="m_3275008586399625363WordSection1">
<p class="MsoNormal"><span style="font-size:11pt">Q2) What does setting the block size bs = 2 accomplish? Because the way to assemble the Jacobian into the system matrix A seems to me no different than I did for the single variable
scalar problem.</span></p></div></div></div></blockquote><div><br></div><div>This is answered above.</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 class="msg3275008586399625363"><div lang="EN-GB" style="overflow-wrap: break-word;"><div class="m_3275008586399625363WordSection1">
<p class="MsoNormal"><span style="font-size:11pt">Kind regards,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Karthik.</span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"><u></u> <u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"><u></u> <u></u></span></p>
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<p class="MsoNormal" style="margin-bottom:12pt"><b><span style="font-size:12pt;color:black">From:
</span></b><span style="font-size:12pt;color:black">Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Date: </b>Sunday, 10 September 2023 at 20:18<br>
<b>To: </b>Chockalingam, Karthikeyan (STFC,DL,HC) <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" target="_blank">karthikeyan.chockalingam@stfc.ac.uk</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] Coupled system of equations on unstructured mesh<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">On Sun, Sep 10, 2023 at 3:15 PM Karthikeyan Chockalingam - STFC UKRI <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" target="_blank">karthikeyan.chockalingam@stfc.ac.uk</a>> wrote:<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">I don’t see an option to give block size.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"><a href="https://petsc.org/release/manualpages/Mat/MatCreateAIJ/" target="_blank">https://petsc.org/release/manualpages/Mat/MatCreateAIJ/</a><u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"><u></u> <u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"><a href="https://petsc.org/release/manualpages/Mat/MatSetBlockSize/" target="_blank">https://petsc.org/release/manualpages/Mat/MatSetBlockSize/</a><u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"><u></u> <u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> Thanks,<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"><u></u> <u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> Matt<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Many thanks,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Karthik.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal" style="margin-bottom:12pt"><b><span style="font-size:12pt;color:black">From:
</span></b><span style="font-size:12pt;color:black">Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Date: </b>Sunday, 10 September 2023 at 20:09<br>
<b>To: </b>Chockalingam, Karthikeyan (STFC,DL,HC) <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" target="_blank">karthikeyan.chockalingam@stfc.ac.uk</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] Coupled system of equations on unstructured mesh</span><span style="font-size:11pt"><u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">On Sun, Sep 10, 2023 at 3:01 PM Karthikeyan Chockalingam - STFC UKRI <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" target="_blank">karthikeyan.chockalingam@stfc.ac.uk</a>>
wrote:<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">I will solve the coupled problem in a non-linear fashion using SNES, so I will have one residual for each variable R(u1) and R(u2) and the resulting
Jacobian matrix<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">J = [J11 J12
<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> J21 J22] for each element.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">For first-order Lagrange elements (in 2D) will have four nodes, then J would be of size 8 x 8. Let's say the variables are u and v. The order would
be [u1 u2 u3 u4 v1 v2 v3 v4].<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Or should I rearrange the above entrées in the element Jacobian so as to have [u1 v1 u2 v2 u3 v3 u4 v4] ordering? In that case, the Jacobian will
not have block ordering I guess.<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">This is the correct order to get block matrices.<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">In my case, the discretization of the u and v are from the same element space.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Can you please elaborate when you say, “Just enlarge the block size of your matrix”?
<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">I have never used block size before and not sure what it accomplishes.
<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Do you mean to say, I should use MATBAIJ instead of MATAIJ?<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">You do not need to change the type, just give the AIJ matrix a blocksize of 2.<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> Thanks,<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> Matt<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">Kind regards,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Karthik.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal" style="margin-bottom:12pt"><b><span style="font-size:12pt;color:black">From:
</span></b><span style="font-size:12pt;color:black">Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Date: </b>Sunday, 10 September 2023 at 19:03<br>
<b>To: </b>Chockalingam, Karthikeyan (STFC,DL,HC) <<a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" target="_blank">karthikeyan.chockalingam@stfc.ac.uk</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] Coupled system of equations on unstructured mesh</span><span style="font-size:11pt"><u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">On Sun, Sep 10, 2023 at 1:48 PM Karthikeyan Chockalingam - STFC UKRI via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a>>
wrote:<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">Hello,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">I have so far solved scalar field problems using finite elements on a given (<b>unstructured</b>) mesh. I made use of
<span style="color:black">MATMPIAIJ</span> to create matrixes, <span class="m_3275008586399625363m4321658602776223612m-5193916087098992094m8670309824937278731s1">
MatCreateVecs</span>(<span class="m_3275008586399625363m4321658602776223612m-5193916087098992094m8670309824937278731s2">A</span>, &<span class="m_3275008586399625363m4321658602776223612m-5193916087098992094m8670309824937278731s2">b</span>, &<span class="m_3275008586399625363m4321658602776223612m-5193916087098992094m8670309824937278731s2">x</span>)
to create vectors, and <span style="color:rgb(108,54,169)">MatZeroRowsColumnsIS </span>to set boundary conditions.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal" style="background:white">
<span style="font-size:11pt;color:black">Now, I would like to solve a coupled system of equations for the quantities u1 and u2 on the (<b>unstructured</b>) mesh. I.e., the matrix should get the double number of rows and columns,
</span><span style="font-size:11pt"><u></u><u></u></span></p>
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<span style="font-size:11pt;color:black"> </span><span style="font-size:11pt"><u></u><u></u></span></p>
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<span style="font-size:11pt;color:black">A = [A00 A01 </span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal" style="background:white">
<span style="font-size:11pt;color:black"> A10 A11]</span><span style="font-size:11pt"><u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">This is usually not a good way to think of it. This division means that all variables of one field come before<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">all those of another. It is much more common to group together all the unknowns at a given point.<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">You could, if the discretizations of u1 and u2 are the same, just enlarge the blocksize of your matrix. Then you set u1 and u2 for each vec location,
or a 2x2 block for each Jacobian location.<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> Thanks,<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> Matt<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal" style="background:white">
<span style="font-size:11pt;color:black">the vectors contain twice the number of entries (e.g. first all u1s and then all u2s). I would like to be sure that the entries of u1 and u2, which are associated with the same element are located on the same processor.</span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal" style="background:white">
<span style="font-size:11pt;color:black"> </span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal" style="background:white">
<span style="font-size:11pt;color:black">Is a pre-defined structure already available within PETSc to enlarge such a single equation to store the entries of coupled equations?</span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">-\Delta u_1+c_{11} u_1+c_{12} u_2=f_1<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">-\Delta u_2+c_{21} u_1+c_{22} u_2=f_2<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal" style="background:white">
<span style="font-size:11pt;color:black">Would I still be able to use </span><span style="font-size:11pt;color:rgb(108,54,169)">MatZeroRowsColumnsIS
</span><span style="font-size:11pt;color:black">u1 and u2 independently to enforce boundary conditions?
</span><span style="font-size:11pt;color:rgb(108,54,169)">MatZeroRowsColumnsIS</span><span style="font-size:11pt;color:black">(</span><span style="font-size:11pt;color:rgb(50,109,116)">A</span><span style="font-size:11pt;color:black">,
</span><span style="font-size:11pt;color:rgb(50,109,116)">is</span><span style="font-size:11pt;color:black">,
</span><span style="font-size:11pt;color:rgb(28,0,207)">1</span><span style="font-size:11pt;color:black">,
</span><span style="font-size:11pt;color:rgb(50,109,116)">x</span><span style="font-size:11pt;color:black">,
</span><span style="font-size:11pt;color:rgb(50,109,116)">b</span><span style="font-size:11pt;color:black">);</span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">I don’t know where to begin. I have so far only been exposed to using
<span style="color:black">MATMPIAIJ and MatSetValues to create and assign values to matrix entries respectively.
</span>I would be grateful if you could provide the stepwise guide.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Kind regards,<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt">Karthik.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11pt"> <u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">-- <u></u><u></u></span></p>
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<p class="MsoNormal"><b><span style="font-size:10.5pt;font-family:Arial,sans-serif;color:rgb(45,45,98)">Karthik Chockalingam, Ph.D.</span></b><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Arial,sans-serif;color:black">Senior Research Software Engineer</span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Arial,sans-serif;color:black">High Performance Systems Engineering Group</span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Arial,sans-serif;color:black">Hartree Centre | Science and Technology Facilities Council</span><span style="font-size:11pt"><u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Arial,sans-serif;color:rgb(33,33,33)"><a href="mailto:karthikeyan.chockalingam@stfc.ac.uk" target="_blank">karthikeyan.chockalingam@stfc.ac.uk</a></span><span style="font-size:11pt"><u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments
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-- Norbert Wiener<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments
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-- Norbert Wiener<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt">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<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-size:11pt"><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><u></u><u></u></span></p>
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</div></blockquote></div><br clear="all"><div><br></div><span class="gmail_signature_prefix">-- </span><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>