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Dear Matt,</div>
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<br>
</div>
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Thank you for your response. This is an idealized setup where I have only one row/column. Sometimes we might need two or even three constraints based on the application. Thus, I will pursue the user-defined IS.</div>
<div class="elementToProof"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">When I supply the IS using the command PCFieldSplitSetIS, I do not specify anything
in the matrix set up right? <br>
</span></div>
<div class="elementToProof"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div class="elementToProof"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Thanks,
<br>
</span></div>
<div class="elementToProof"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Pantelis<br>
</span></div>
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<div dir="ltr" id="divRplyFwdMsg"><span style="font-family: Calibri, sans-serif; font-size: 11pt; color: rgb(0, 0, 0);"><b>Από:</b> Matthew Knepley <knepley@gmail.com><br>
<b>Στάλθηκε:</b> Τρίτη, 23 Ιανουαρίου 2024 2:51 μμ<br>
<b>Προς:</b> Pantelis Moschopoulos <pmoschopoulos@outlook.com><br>
<b>Κοιν.:</b> Barry Smith <bsmith@petsc.dev>; petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Θέμα:</b> Re: [petsc-users] Question about a parallel implementation of PCFIELDSPLIT</span>
<div> </div>
</div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">On Tue, Jan 23, 2024 at 4:23 AM Pantelis Moschopoulos <<a href="mailto:pmoschopoulos@outlook.com" id="OWA0bb35ae1-4377-ea37-16e5-d213bc235f5f" class="OWAAutoLink">pmoschopoulos@outlook.com</a>>
wrote:</span></div>
<blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left: 1px solid rgb(204, 204, 204);">
<div style="direction: ltr; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Dear Matt and Dear Barry,</div>
<div style="direction: ltr; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">I have some follow up questions regarding FieldSplit. </span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Let's assume that I solve again the 3D Stokes flow but now I have also a global constraint
that controls the flow rate at the inlet. Now, the matrix has the same unknowns as before, i.e. ux0,uy0,uz0,p0//ux1,uy1,uz1,p1//..., but the last line (and the last column) corresponds to the contribution of the global constraint equation. I want to incorporate
the last line (and last column) into the local block of velocities (split 0) and the pressure. The problem is how I do that. I have two questions:</span></div>
<ol start="1" style="direction: ltr; list-style-type: decimal;" data-listchain="__List_Chain_225">
<li style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); direction: ltr;">
<span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Now, the block size should be 5 in the matrix and vector creation for this problem?</span></li></ol>
</blockquote>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">No. Blocksize is only useful when the vector/matrix layout is completely regular, meaning
_every_ block looks the same. Here you have a single row to be added in.</span></div>
<blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left: 1px solid rgb(204, 204, 204);">
<ol start="1" style="direction: ltr; list-style-type: decimal;" data-listchain="__List_Chain_226">
<li style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); direction: ltr;">
<span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">I have to rely entirely on PCFieldSplitSetIS to create the two blocks? Can I augment simply the previously defined
block 0 with the last line of the matrix?</span></li></ol>
</blockquote>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">If you want to add in a single row, then you have to specify the IS yourself since
we cannot generate it from the regular pattern.</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">However, if you know that you will only ever have a single constraint row (which I
assume is fairly dense), then I would suggest instead using MatLRC, which Jose developed for SLEPc. This handles the last row/col as a low-rank correction. One step of Sherman-Morrison-Woobury solves this exactly. It requires a solve for A, for which you can
use FieldSplit as normal.</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> Thanks,</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> Matt</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> </span></div>
<blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left: 1px solid rgb(204, 204, 204);">
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Up to this moment, I use the following commands to create the Field split:</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">ufields(3) = [0, 1, 2]<br>
pfields(1) = [3]</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">call PCSetType(pc, PCFIELDSPLIT, ierr)</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">call PCFieldSplitSetBlockSize(pc, 4,ierr)</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> call PCFieldSplitSetFields(pc, "0", 3, ufields, ufields,ierr)</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> call PCFieldSplitSetFields(pc, "1", 1, pfields, pfields,ierr)</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Thanks,</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Pantelis</span></div>
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</span></div>
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</span></div>
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<div dir="ltr" id="x_m_-3462641011636893950divRplyFwdMsg"><span style="font-family: Calibri, sans-serif; font-size: 11pt; color: rgb(0, 0, 0);"><b>Από:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" id="OWA1dd8061b-9e70-52aa-8f36-5486331287dd" class="OWAAutoLink">knepley@gmail.com</a>><br>
<b>Στάλθηκε:</b> Παρασκευή, 19 Ιανουαρίου 2024 11:31 μμ<br>
<b>Προς:</b> Barry Smith <<a href="mailto:bsmith@petsc.dev" id="OWA10c7918c-8c37-fd2f-9580-474232da7c4b" class="OWAAutoLink">bsmith@petsc.dev</a>><br>
<b>Κοιν.:</b> Pantelis Moschopoulos <<a href="mailto:pmoschopoulos@outlook.com" id="OWA2dedc01b-a413-7fc8-f7b2-bcaf8abadc0b" class="OWAAutoLink">pmoschopoulos@outlook.com</a>>;
<a href="mailto:petsc-users@mcs.anl.gov" id="OWA3a97493d-4234-6a48-666e-cd83d5592b42" class="OWAAutoLink">
petsc-users@mcs.anl.gov</a> <<a href="mailto:petsc-users@mcs.anl.gov" id="OWAb3f6c5ea-26df-6678-b94f-13cad3bac763" class="OWAAutoLink">petsc-users@mcs.anl.gov</a>><br>
<b>Θέμα:</b> Re: [petsc-users] Question about a parallel implementation of PCFIELDSPLIT</span>
<div> </div>
</div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">On Fri, Jan 19, 2024 at 4:25 PM Barry Smith <<a href="mailto:bsmith@petsc.dev" id="OWAe0edb880-f66d-945d-0a72-132eb4014cb6" class="OWAAutoLink">bsmith@petsc.dev</a>>
wrote:</span></div>
<blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left: 1px solid rgb(204, 204, 204);">
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> Generally fieldsplit is used on problems that have a natural "split" of the variables
into two or more subsets. For example u0,v0,u1,v1,u2,v2,u3,v4 This is often indicated in the vectors and matrices with the "blocksize" argument, 2 in this case. DM also often provides this information. </span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> When laying out a vector/matrix with a blocksize one must ensure that an equal number
of of the subsets appears on each MPI process. So, for example, if the above vector is distributed over 3 MPI processes one could use u0,v0,u1,v1 u2,v2 u3,v3 but one cannot use u0,v0,u1 v1,u2,v2 u3,v3. Another way to think about it is that
one must split up the vector as indexed by block among the processes. For most multicomponent problems this type of decomposition is very natural in the logic of the code.</span></div>
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<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">This blocking is only convenient, not necessary. You can specify your own field division
using PCFieldSplitSetIS().</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> Thanks,</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> Matt</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> </span></div>
<blockquote style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left: 1px solid rgb(204, 204, 204);">
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> Barry</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"> </span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<blockquote>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">On Jan 19, 2024, at 3:19 AM, Pantelis Moschopoulos <<a href="mailto:pmoschopoulos@outlook.com" id="OWAc9999050-e32e-9552-b581-2d3c3ab0d52c" class="OWAAutoLink">pmoschopoulos@outlook.com</a>>
wrote:</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr; text-align: left; white-space: normal; letter-spacing: normal; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; font-weight: 400;">
<span style="letter-spacing: normal; color: rgb(0, 0, 0);">Dear all,</span></div>
<div style="direction: ltr; text-align: left; white-space: normal; letter-spacing: normal; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; font-weight: 400;">
<span style="letter-spacing: normal; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr; text-align: left; white-space: normal; letter-spacing: normal; font-family: Helvetica; font-size: 18px; font-weight: 400;">
<span style="letter-spacing: normal; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">When I am using PCFIELDSPLIT and pc type "schur" in serial mode everything works fine. When
I turn now to parallel, I observe that the number of ranks that I can use must divide the number of N without any remainder, where N is the number of unknowns. Otherwise, an error of the following form emerges: "Local columns of A10 3473 do not equal local
rows of A00 3471".</span></div>
<div style="direction: ltr; text-align: left; white-space: normal; letter-spacing: normal; font-family: Helvetica; font-size: 18px; font-weight: 400;">
<span style="letter-spacing: normal; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr; text-align: left; white-space: normal; letter-spacing: normal; font-family: Helvetica; font-size: 18px; font-weight: 400;">
<span style="letter-spacing: normal; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Can I do something to overcome this?</span></div>
<div style="direction: ltr; text-align: left; white-space: normal; letter-spacing: normal; font-family: Helvetica; font-size: 18px; font-weight: 400;">
<span style="letter-spacing: normal; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr; text-align: left; white-space: normal; letter-spacing: normal; font-family: Helvetica; font-size: 18px; font-weight: 400;">
<span style="letter-spacing: normal; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Thanks,</span></div>
<div style="direction: ltr; text-align: left; white-space: normal; letter-spacing: normal; font-family: Helvetica; font-size: 18px; font-weight: 400;">
<span style="letter-spacing: normal; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Pantelis</span></div>
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</span></div>
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</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">--</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">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</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><a href="http://www.cse.buffalo.edu/~knepley/" id="OWA1287698b-8732-c37b-1e96-69cca82d74cf" class="OWAAutoLink" data-auth="NotApplicable">https://www.cse.buffalo.edu/~knepley/</a></span></div>
</blockquote>
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</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br>
</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">--</span></div>
<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">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</span></div>
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<div style="direction: ltr;"><span style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><a href="http://www.cse.buffalo.edu/~knepley/" id="OWA85a7251d-1ad7-c199-9fc4-fd8e74ea3d1e" class="OWAAutoLink" data-auth="NotApplicable">https://www.cse.buffalo.edu/~knepley/</a></span></div>
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