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<p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial">Hi,<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span style="font-size:10.0pt;
font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">I am working on an application that requires the inversion of an implicit operator that is more or less a very anisotropic 3D diffusion operator
(about 1E6 ratio between diffusion coefficient in 1 direction with respect to the 2 others). The matrix is therefore very badly conditioned. By direction splitting, I can split the system in 2 pieces:<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">A = B + C<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">where B is block diagonal and contains all the coefficients corresponding to the high diffusion part of the operator. B seems like a good preconditioner
for the system (I checked in low resolution cases with matlab that applying B^-1 to A reduces its condition number by a factor of close to 1E6), but B is ill-conditioned. However, since it is block diagonal and that it will not vary in time (contrary to C),
it seems to me that it would be a good idea to perform once and for all an LU factorization of B and use it to precondition A each time the ksp solver is called afterwards.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">I somehow can’t figure out how to do this in practise with PETSC. I tried to configure the KSP like this<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">call KSPSetOperators(myKSP,A,B,SAME_PRECONDITIONER,ierr)
<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">and then run PETSC with the following options:<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">-pc_type asm -sub_pc_type lu -ksp_type bcgsl<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">but the computation time becomes awful, far more than if I try to do separately the LU decomposition of the blocks of B with MUMPS.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">Would you have some advice / hints on how to implement such a preconditioner for my problem?<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">Thanks in advance.<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial"><o:p> </o:p></span></font></p>
<p class="MsoNormal"><font size="2" face="Arial"><span lang="EN-GB" style="font-size:
10.0pt;font-family:Arial">Patrick<o:p></o:p></span></font></p>
<p class="MsoNormal"><font size="3" face="Times New Roman"><span style="font-size:
12.0pt"><o:p> </o:p></span></font></p>
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