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Hello,</div>
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I am working to solve Stokes problem on a domain that is discretized using two different types of mesh. A part of the mesh uses fem formulation and the rest uses nodal integral method (NIM) formulation (the details of which I will skip). However, the key takeaway
is that NIM formulation of stokes uses pressure Poisson formulation instead of the continuity equation while FEM formulation uses the continuity equation. They are coupled at the interface. Right now, I am building a single matrix for the entire domain and
solving it using fieldsplit option in a nested fashion. The matrix structure and the unknown vector are shown below. </div>
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My questions are:</div>
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<li><font color="#000000" face="Calibri, Arial, Helvetica, sans-serif"><span style="caret-color: rgb(0, 0, 0);">Are there any basic guidelines to solve these kind of problems.</span></font></li><li><font color="#000000" face="Calibri, Arial, Helvetica, sans-serif"><span style="caret-color: rgb(0, 0, 0);">As I have mentioned I am currently using nested fieldsplit. The first split is using indices and the other split is done using detect saddle point
option. is there a way to avoid using that option and doing it by combining set of indices or fields.</span></font><span style="caret-color: rgb(0, 0, 0); background: var(--white);"> </span></li></ul>
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The matrix structure is </div>
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[A<sub>u_fem </sub>B<sub>p_fem</sub> 0 0]</div>
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[C<sub>u_fem. </sub>0 0 0]</div>
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[0 0 D<sub>u_nim </sub>E<sub>p_nim</sub>]</div>
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<span style="font-size: 12pt;">[0 0 0 F<sub>p_nim</sub>]</span></div>
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<span style="font-size: 12pt;">the unknown vector is given by</span></div>
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<span style="font-size: 12pt;">[u<sub>fem</sub> p<sub>fem</sub> u<sub>nim</sub> p<sub>nim</sub>]</span></div>
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<span style="font-size: 12pt;">Let me know if any additional information is needed.</span></div>
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<span style="font-size: 12pt;">Thanks,<br>
Solomon.</span></div>
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