[petsc-users] MATSOLVERSUPERLU_DIST not giving the correct solution

[Justin Dong]

I actually was able to solve my own problem...for some reason, I need to do

PCSetType(pc, PCLU);
PCFactorSetMatSolverPackage(pc, MATSOLVERSUPERLU_DIST);
KSPSetTolerances(ksp, 1.e-15, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT);

instead of the ordering I initially had, though I'm not really clear on
what the issue was. However, there seems to be some loss of accuracy as I
increase the number of processes. Is this expected, or can I force a lower
tolerance somehow? I am able to compare the solutions to a reference
solution, and the error increases as I increase the processes. This is the
solution in sequential:

superlu_1process = [
-6.8035811950925553e-06
1.6324030474375778e-04
5.4145340579614926e-02
1.6640521936281516e-04
-1.7669374392923965e-04
-2.8099208957838207e-04
5.3958133511222223e-02
-5.4077899123806263e-02
-5.3972905090366369e-02
-1.9485020474821160e-04
5.4239813043824400e-02
4.4883984259948430e-04];

superlu_2process = [
-6.8035811950509821e-06
1.6324030474371623e-04
5.4145340579605655e-02
1.6640521936281687e-04
-1.7669374392923807e-04
-2.8099208957839834e-04
5.3958133511212911e-02
-5.4077899123796964e-02
-5.3972905090357078e-02
-1.9485020474824480e-04
5.4239813043815172e-02
4.4883984259953320e-04];

superlu_4process= [
-6.8035811952565206e-06
1.6324030474386164e-04
5.4145340579691455e-02
1.6640521936278326e-04
-1.7669374392921441e-04
-2.8099208957829171e-04
5.3958133511299078e-02
-5.4077899123883062e-02
-5.3972905090443085e-02
-1.9485020474806352e-04
5.4239813043900860e-02
4.4883984259921287e-04];

This is some finite element solution and I can compute the error of the
solution against an exact solution in the functional L2 norm:

error with 1 process:    1.71340e-02 (accepted value)
error with 2 processes: 2.65018e-02
error with 3 processes: 3.00164e-02
error with 4 processes: 3.14544e-02


Is there a way to remedy this?


On Wed, Apr 30, 2014 at 2:37 AM, Justin Dong <jsd1 at rice.edu> wrote:

> Hi,
>
> I'm trying to solve a linear system in parallel using SuperLU but for some
> reason, it's not giving me the correct solution. I'm testing on a small
> example so I can compare the sequential and parallel cases manually. I'm
> absolutely sure that my routine for generating the matrix and right-hand
> side in parallel is working correctly.
>
> Running with 1 process and PCLU gives the correct solution. Running with 2
> processes and using SUPERLU_DIST does not give the correct solution (I
> tried with 1 process too but according to the superlu documentation, I
> would need SUPERLU for sequential?). This is the code for solving the
> system:
>
>         /* solve the system */
> KSPCreate(PETSC_COMM_WORLD, &ksp);
> KSPSetOperators(ksp, Aglobal, Aglobal, DIFFERENT_NONZERO_PATTERN);
>  KSPSetType(ksp,KSPPREONLY);
>
> KSPGetPC(ksp, &pc);
>
> KSPSetTolerances(ksp, 1.e-13, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT);
>  PCFactorSetMatSolverPackage(pc, MATSOLVERSUPERLU_DIST);
>
> KSPSolve(ksp, bglobal, bglobal);
>
> Sincerely,
> Justin
>
>
>
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