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<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">I have a block matrix [A, B; C, D], and I want to use Schur complement to solve the linear system [A, B; C, D] * [x; y] = [c; d].
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<div>I want to apply a preconditioner for solving ( D - C*A^(-1)*B ) y = rhs. And it is easy for me to find an A' which is approximate to A, and A'^(-1) is easy to get. So for this part, I can easily define a preconditioner matrix P = <span style="font-size: 10pt;">(
D - C*A'^(-1)*B ) using </span><span style="font-family: Menlo; font-size: 11px;">PCFieldSplitSchurPrecondition</span><span style="font-size: 10pt;">. The next step is that I want to do incomplete LU factorization for </span><span style="font-size: 10pt;">P
as my left and right preconditioner for solving </span><span style="font-size: 10pt;">( D - C*A^(-1)*B ) y = rhs using gmres or bcgs. </span></div>
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<div><span style="font-size: 10pt;">My question is since part of the PC is user defined, and part of it is PETSC defined, how can I combine them? Can I do something like:</span></div>
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ierr = PCFieldSplitSchurPrecondition(pc, PC_FIELDSPLIT_SCHUR_PRE_USER, P);CHKERRQ(ierr);</p>
<pre width="80" style="background-color: rgb(255, 255, 255);"><span style="font-family: Menlo; font-size: 11px;">ierr = PCSetType(pc, PCILU);CHKERRQ(ierr);</span></pre>
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<div><span style="font-size: 10pt;">Hui</span></div>
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