[petsc-users] MATSOLVERSUPERLU_DIST not giving the correct solution
Justin Dong
jsd1 at rice.edu
Wed Apr 30 17:28:05 CDT 2014
Problem solved. It as user error on my part. The parallel solve was working
correctly but when I was computing the functional errors, I needed to
extract an array from the solution vector. Not all of the processes had
finished assembling yet, so I think that caused some problems with the
array.
I'm noticing though that superlu_dist is taking longer than just using PCLU
in sequential. Using the time function in Mac terminal:
34.59 real 8.12 user 7.76 sys
34.59 real 8.74 user 7.87 sys
34.60 real 8.06 user 7.80 sys
34.59 real 8.84 user 7.77 sys
In sequential:
17.22 real 16.79 user 0.23 sys
Is this at all expected? My code is around 2x faster in parallel (on a dual
core machine). I tried -pc_type redundant -redundant_pc_type lu but that
didn't speed up the parallel case.
On Wed, Apr 30, 2014 at 1:19 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
> Please send the same thing on one process.
>
>
> On 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:
> >
> > 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
> >
> >
>
>
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