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<p class="MsoNormal"><span style="font-size:11.0pt">I am trying to solve the Stokes equation with the Brinkman term to simulate a solid material. My intention is to implement the preconditioner in this paper:
<a href="https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.426section%202.6">https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.426</a> (section 2.6) where they solve for the velocity and substitute that expression in the pressure equation. They end up
solving a system of the type B K^-1 B^T, i.e. the Schur complement of the problem. For this system of equations, they argue that the preconditioner in page 11 is perfect for a given constant Brinkman penalty term.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Because I am solving for velocity and pressure without doing any substitution, I thought I could use a PC fieldsplit type Schur (full factorization) and provide the preconditioner in the paper to solve the
Schur complement. My question is, should I provide this preconditioner through PCFieldSplitSetSchurPre or through fieldsplit_1_pc_type (probably through the Firedrake interface as in
<a href="https://www.firedrakeproject.org/demos/stokes.py.html">https://www.firedrakeproject.org/demos/stokes.py.html</a>) ?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Thanks<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Miguel<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">Miguel A. Salazar de Troya</span><span style="font-size:10.5pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">Postdoctoral Researcher, Lawrence Livermore National Laboratory</span><span style="font-size:10.5pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">B141</span><span style="font-size:10.5pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">Rm: 1085-5</span><span style="font-size:10.5pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Consolas;color:black">Ph: 1(925) 422-6411</span><o:p></o:p></p>
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