[petsc-users] MATSOLVERSUPERLU_DIST not giving the correct solution

Matthew Knepley knepley at gmail.com
Wed Apr 30 08:42:36 CDT 2014 

On Wed, Apr 30, 2014 at 8:17 AM, Justin Dong <jsd1 at rice.edu> wrote:

> Here are the results of one example where the solution is incorrect:
>

I am skeptical of your conclusion. The entry in "true residual norm",
4.545226736905e-16, is generated
using just MatMult() and VecAXPY(). It is the definition of "correct". What
do you get when you replicate
these steps with the solution that is returned?

   Matt


>   0 KSP unpreconditioned resid norm 7.267616711036e-05 true resid norm
> 7.267616711036e-05 ||r(i)||/||b|| 1.000000000000e+00
>
>   1 KSP unpreconditioned resid norm 4.081398605668e-16 true resid norm
> 4.017029301117e-16 ||r(i)||/||b|| 5.527299334618e-12
>
>   2 KSP unpreconditioned resid norm 4.378737248697e-21 true resid norm
> 4.545226736905e-16 ||r(i)||/||b|| 6.254081520291e-12
>
> KSP Object: 4 MPI processes
>
>   type: gmres
>
>     GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
>
>     GMRES: happy breakdown tolerance 1e-30
>
>   maximum iterations=10000, initial guess is zero
>
>   tolerances:  relative=1e-13, absolute=1e-50, divergence=10000
>
>   right preconditioning
>
>   using UNPRECONDITIONED norm type for convergence test
>
> PC Object: 4 MPI processes
>
>   type: lu
>
>     LU: out-of-place factorization
>
>     tolerance for zero pivot 2.22045e-14
>
>     matrix ordering: natural
>
>     factor fill ratio given 0, needed 0
>
>       Factored matrix follows:
>
>         Matrix Object:         4 MPI processes
>
>           type: mpiaij
>
>           rows=1536, cols=1536
>
>           package used to perform factorization: superlu_dist
>
>           total: nonzeros=0, allocated nonzeros=0
>
>           total number of mallocs used during MatSetValues calls =0
>
>             SuperLU_DIST run parameters:
>
>               Process grid nprow 2 x npcol 2
>
>               Equilibrate matrix TRUE
>
>               Matrix input mode 1
>
>               Replace tiny pivots TRUE
>
>               Use iterative refinement FALSE
>
>               Processors in row 2 col partition 2
>
>               Row permutation LargeDiag
>
>               Column permutation METIS_AT_PLUS_A
>
>               Parallel symbolic factorization FALSE
>
>               Repeated factorization SamePattern_SameRowPerm
>
>   linear system matrix = precond matrix:
>
>   Matrix Object:   4 MPI processes
>
>     type: mpiaij
>
>     rows=1536, cols=1536
>
>     total: nonzeros=17856, allocated nonzeros=64512
>
>     total number of mallocs used during MatSetValues calls =0
>
>       using I-node (on process 0) routines: found 128 nodes, limit used is
> 5
>
>
> On Wed, Apr 30, 2014 at 7:57 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>
>> On Apr 30, 2014, at 6:46 AM, Matthew Knepley <knepley at gmail.com> wrote:
>>
>> > On Wed, Apr 30, 2014 at 6:19 AM, Justin Dong <jsd1 at rice.edu> wrote:
>> > Thanks. If I turn on the Krylov solver, the issue still seems to
>> persist though.
>> >
>> > mpiexec -n 4 -ksp_type gmres -ksp_rtol 1.0e-13 -pc_type lu
>> -pc_factor_mat_solver_package superlu_dist
>> >
>> > I'm testing on a very small system now (24 ndofs), but if I go larger
>> (around 20000 ndofs) then it gets worse.
>> >
>> > For the small system, I exported the matrices to matlab to make sure
>> they were being assembled correct in parallel, and I'm certain that that
>> they are.
>> >
>> > For convergence questions, always run using -ksp_monitor -ksp_view so
>> that we can see exactly what you run.
>>
>>   Also run with -ksp_pc_side right
>>
>>
>> >
>> >   Thanks,
>> >
>> >      Matt
>> >
>> >
>> > On Wed, Apr 30, 2014 at 5:32 AM, Matthew Knepley <knepley at gmail.com>
>> wrote:
>> > On Wed, Apr 30, 2014 at 3:02 AM, Justin Dong <jsd1 at rice.edu> wrote:
>> > 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);
>> >
>> > 1) Before you do SetType(PCLU) the preconditioner has no type, so
>> FactorSetMatSolverPackage() has no effect
>> >
>> > 2) There is a larger issue here. Never ever ever ever code in this way.
>> Hardcoding a solver is crazy. The solver you
>> >      use should depend on the equation, discretization, flow regime,
>> and architecture. Recompiling for all those is
>> >      out of the question. You should just use
>> >
>> >     KSPCreate()
>> >     KSPSetOperators()
>> >     KSPSetFromOptions()
>> >     KSPSolve()
>> >
>> > and then
>> >
>> >    -pc_type lu -pc_factor_mat_solver_package superlu_dist
>> >
>> >
>> > 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:
>> >
>> > Yes, this is unavoidable. However, just turn on the Krylov solver
>> >
>> >   -ksp_type gmres -ksp_rtol 1.0e-10
>> >
>> > and you can get whatever residual tolerance you want. To get a specific
>> error, you would need
>> > a posteriori error estimation, which you could include in a custom
>> convergence criterion.
>> >
>> >   Thanks,
>> >
>> >      Matt
>> >
>> > 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
>> >
>> >
>> >
>> >
>> >
>> >
>> > --
>> > What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> > -- Norbert Wiener
>> >
>> >
>> >
>> >
>> > --
>> > What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> > -- Norbert Wiener
>>
>>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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