<div dir="ltr">Another option are the PCPATCH solvers for multigrid, as shown in this paper: <a href="https://arxiv.org/abs/1912.08516">https://arxiv.org/abs/1912.08516</a><div>which I believe solves incompressible elasticity. There is an example in PETSc for Stokes I believe.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Sep 26, 2022 at 5:20 AM 晓峰 何 <<a href="mailto:tlanyan@hotmail.com">tlanyan@hotmail.com</a>> wrote:<br></div><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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<span style="font-family:STSongti-SC-Regular">Are there other approaches to solve this kind of systems in PETSc except for field-split methods? </span>
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<div style="font-family:STSongti-SC-Regular">Thanks,</div>
<div style="font-family:STSongti-SC-Regular">Xiaofeng</div>
<div><br>
<blockquote type="cite">
<div>On Sep 26, 2022, at 14:13, Jed Brown <<a href="mailto:jed@jedbrown.org" target="_blank">jed@jedbrown.org</a>> wrote:</div>
<br>
<div><span style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;float:none;display:inline">This
is the joy of factorization field-split methods. The actual Schur complement is dense, so we represent it implicitly. A common strategy is to assemble the mass matrix and drop it in the 11 block of the Pmat. You can check out some examples in the repository
for incompressible flow (Stokes problems). The LSC (least squares commutator) is another option. You'll likely find that lumping diag(A00)^{-1} works poorly because the resulting operator behaves like a Laplacian rather than like a mass matrix.</span><br style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none">
<br style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none">
<span style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;float:none;display:inline">晓峰
何 <</span><a href="mailto:tlanyan@hotmail.com" style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px" target="_blank">tlanyan@hotmail.com</a><span style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;float:none;display:inline">>
writes:</span><br style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none">
<br style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none">
<blockquote type="cite" style="font-family:STSongti-SC-Regular;font-size:18px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none">
If assigned a preconditioner to A11 with this cmd options:<br>
<br>
-fieldsplit_0_ksp_type gmres -fieldsplit_0_pc_type ilu -fieldsplit_1_ksp_type gmres -fieldsplit_1_pc_type ilu<br>
<br>
Then I got this error:<br>
<br>
"Could not locate a solver type for factorization type ILU and matrix type schurcomplement"<br>
<br>
How could I specify a preconditioner for A11?<br>
<br>
BR,<br>
Xiaofeng<br>
<br>
<br>
On Sep 26, 2022, at 11:02, 晓峰 何 <<a href="mailto:tlanyan@hotmail.com" target="_blank">tlanyan@hotmail.com</a><<a href="mailto:tlanyan@hotmail.com" target="_blank">mailto:tlanyan@hotmail.com</a>>> wrote:<br>
<br>
-fieldsplit_0_ksp_type gmres -fieldsplit_0_pc_type ilu -fieldsplit_1_ksp_type gmres -fieldsplit_1_pc_type none</blockquote>
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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>