[petsc-users] superlu_dist produces random results
Smith, Barry F.
bsmith at mcs.anl.gov
Wed Nov 15 16:35:41 CST 2017
Since the convergence labeled linear does not converge to 14 digits in one iteration I am assuming you are using lagged preconditioning and or lagged Jacobian?
What happens if you do no lagging and solve each linear solve with a new LU factorization?
Barry
> On Nov 15, 2017, at 4:24 PM, Kong, Fande <fande.kong at inl.gov> wrote:
>
>
>
> On Wed, Nov 15, 2017 at 2:52 PM, Smith, Barry F. <bsmith at mcs.anl.gov> wrote:
>
>
> > On Nov 15, 2017, at 3:36 PM, Kong, Fande <fande.kong at inl.gov> wrote:
> >
> > Hi Barry,
> >
> > Thanks for your reply. I was wondering why this happens only when we use superlu_dist. I am trying to understand the algorithm in superlu_dist. If we use ASM or MUMPS, we do not produce these differences.
> >
> > The differences actually are NOT meaningless. In fact, we have a real transient application that presents this issue. When we run the simulation with superlu_dist in parallel for thousands of time steps, the final physics solution looks totally different from different runs. The differences are not acceptable any more. For a steady problem, the difference may be meaningless. But it is significant for the transient problem.
>
> I submit that the "physics solution" of all of these runs is equally right and equally wrong. If the solutions are very different due to a small perturbation than something is wrong with the model or the integrator, I don't think you can blame the linear solver (see below)
> >
> > This makes the solution not reproducible, and we can not even set a targeting solution in the test system because the solution is so different from one run to another. I guess there might/may be a tiny bug in superlu_dist or the PETSc interface to superlu_dist.
>
> This is possible but it is also possible this is due to normal round off inside of SuperLU dist.
>
> Since you have SuperLU_Dist inside a nonlinear iteration it shouldn't really matter exactly how well SuperLU_Dist does. The nonlinear iteration does essential defect correction for you; are you making sure that the nonlinear iteration always works for every timestep? For example confirm that SNESGetConvergedReason() is always positive.
>
> Definitely it could be something wrong on my side. But let us focus on the simple question first.
>
> To make the discussion a little simpler, let us back to the simple problem (heat conduction). Now I want to understand why this happens to superlu_dist only. When we are using ASM or MUMPS, why we can not see the differences from one run to another? I posted the residual histories for MUMPS and ASM. We can not see any differences in terms of the residual norms when using MUMPS or ASM. Does superlu_dist have higher round off than other solvers?
>
>
>
> MUMPS run1:
>
> 0 Nonlinear |R| = 9.447423e+03
> 0 Linear |R| = 9.447423e+03
> 1 Linear |R| = 1.013384e-02
> 2 Linear |R| = 4.020993e-08
> 1 Nonlinear |R| = 1.404678e-02
> 0 Linear |R| = 1.404678e-02
> 1 Linear |R| = 4.836162e-08
> 2 Linear |R| = 7.055620e-14
> 2 Nonlinear |R| = 4.836392e-08
>
> MUMPS run2:
>
> 0 Nonlinear |R| = 9.447423e+03
> 0 Linear |R| = 9.447423e+03
> 1 Linear |R| = 1.013384e-02
> 2 Linear |R| = 4.020993e-08
> 1 Nonlinear |R| = 1.404678e-02
> 0 Linear |R| = 1.404678e-02
> 1 Linear |R| = 4.836162e-08
> 2 Linear |R| = 7.055620e-14
> 2 Nonlinear |R| = 4.836392e-08
>
> MUMPS run3:
>
> 0 Nonlinear |R| = 9.447423e+03
> 0 Linear |R| = 9.447423e+03
> 1 Linear |R| = 1.013384e-02
> 2 Linear |R| = 4.020993e-08
> 1 Nonlinear |R| = 1.404678e-02
> 0 Linear |R| = 1.404678e-02
> 1 Linear |R| = 4.836162e-08
> 2 Linear |R| = 7.055620e-14
> 2 Nonlinear |R| = 4.836392e-08
>
> MUMPS run4:
>
> 0 Nonlinear |R| = 9.447423e+03
> 0 Linear |R| = 9.447423e+03
> 1 Linear |R| = 1.013384e-02
> 2 Linear |R| = 4.020993e-08
> 1 Nonlinear |R| = 1.404678e-02
> 0 Linear |R| = 1.404678e-02
> 1 Linear |R| = 4.836162e-08
> 2 Linear |R| = 7.055620e-14
> 2 Nonlinear |R| = 4.836392e-08
>
>
>
> ASM run1:
>
> 0 Nonlinear |R| = 9.447423e+03
> 0 Linear |R| = 9.447423e+03
> 1 Linear |R| = 6.189229e+03
> 2 Linear |R| = 3.252487e+02
> 3 Linear |R| = 3.485174e+01
> 4 Linear |R| = 8.600695e+00
> 5 Linear |R| = 3.333942e+00
> 6 Linear |R| = 1.706112e+00
> 7 Linear |R| = 5.047863e-01
> 8 Linear |R| = 2.337297e-01
> 9 Linear |R| = 1.071627e-01
> 10 Linear |R| = 4.692177e-02
> 11 Linear |R| = 1.340717e-02
> 12 Linear |R| = 4.753951e-03
> 1 Nonlinear |R| = 2.320271e-02
> 0 Linear |R| = 2.320271e-02
> 1 Linear |R| = 4.367880e-03
> 2 Linear |R| = 1.407852e-03
> 3 Linear |R| = 6.036360e-04
> 4 Linear |R| = 1.867661e-04
> 5 Linear |R| = 8.760076e-05
> 6 Linear |R| = 3.260519e-05
> 7 Linear |R| = 1.435418e-05
> 8 Linear |R| = 4.532875e-06
> 9 Linear |R| = 2.439053e-06
> 10 Linear |R| = 7.998549e-07
> 11 Linear |R| = 2.428064e-07
> 12 Linear |R| = 4.766918e-08
> 13 Linear |R| = 1.713748e-08
> 2 Nonlinear |R| = 3.671573e-07
>
>
> ASM run2:
>
> 0 Nonlinear |R| = 9.447423e+03
> 0 Linear |R| = 9.447423e+03
> 1 Linear |R| = 6.189229e+03
> 2 Linear |R| = 3.252487e+02
> 3 Linear |R| = 3.485174e+01
> 4 Linear |R| = 8.600695e+00
> 5 Linear |R| = 3.333942e+00
> 6 Linear |R| = 1.706112e+00
> 7 Linear |R| = 5.047863e-01
> 8 Linear |R| = 2.337297e-01
> 9 Linear |R| = 1.071627e-01
> 10 Linear |R| = 4.692177e-02
> 11 Linear |R| = 1.340717e-02
> 12 Linear |R| = 4.753951e-03
> 1 Nonlinear |R| = 2.320271e-02
> 0 Linear |R| = 2.320271e-02
> 1 Linear |R| = 4.367880e-03
> 2 Linear |R| = 1.407852e-03
> 3 Linear |R| = 6.036360e-04
> 4 Linear |R| = 1.867661e-04
> 5 Linear |R| = 8.760076e-05
> 6 Linear |R| = 3.260519e-05
> 7 Linear |R| = 1.435418e-05
> 8 Linear |R| = 4.532875e-06
> 9 Linear |R| = 2.439053e-06
> 10 Linear |R| = 7.998549e-07
> 11 Linear |R| = 2.428064e-07
> 12 Linear |R| = 4.766918e-08
> 13 Linear |R| = 1.713748e-08
> 2 Nonlinear |R| = 3.671573e-07
>
> ASM run3:
>
> 0 Nonlinear |R| = 9.447423e+03
> 0 Linear |R| = 9.447423e+03
> 1 Linear |R| = 6.189229e+03
> 2 Linear |R| = 3.252487e+02
> 3 Linear |R| = 3.485174e+01
> 4 Linear |R| = 8.600695e+00
> 5 Linear |R| = 3.333942e+00
> 6 Linear |R| = 1.706112e+00
> 7 Linear |R| = 5.047863e-01
> 8 Linear |R| = 2.337297e-01
> 9 Linear |R| = 1.071627e-01
> 10 Linear |R| = 4.692177e-02
> 11 Linear |R| = 1.340717e-02
> 12 Linear |R| = 4.753951e-03
> 1 Nonlinear |R| = 2.320271e-02
> 0 Linear |R| = 2.320271e-02
> 1 Linear |R| = 4.367880e-03
> 2 Linear |R| = 1.407852e-03
> 3 Linear |R| = 6.036360e-04
> 4 Linear |R| = 1.867661e-04
> 5 Linear |R| = 8.760076e-05
> 6 Linear |R| = 3.260519e-05
> 7 Linear |R| = 1.435418e-05
> 8 Linear |R| = 4.532875e-06
> 9 Linear |R| = 2.439053e-06
> 10 Linear |R| = 7.998549e-07
> 11 Linear |R| = 2.428064e-07
> 12 Linear |R| = 4.766918e-08
> 13 Linear |R| = 1.713748e-08
> 2 Nonlinear |R| = 3.671573e-07
>
>
>
> ASM run4:
> 0 Nonlinear |R| = 9.447423e+03
> 0 Linear |R| = 9.447423e+03
> 1 Linear |R| = 6.189229e+03
> 2 Linear |R| = 3.252487e+02
> 3 Linear |R| = 3.485174e+01
> 4 Linear |R| = 8.600695e+00
> 5 Linear |R| = 3.333942e+00
> 6 Linear |R| = 1.706112e+00
> 7 Linear |R| = 5.047863e-01
> 8 Linear |R| = 2.337297e-01
> 9 Linear |R| = 1.071627e-01
> 10 Linear |R| = 4.692177e-02
> 11 Linear |R| = 1.340717e-02
> 12 Linear |R| = 4.753951e-03
> 1 Nonlinear |R| = 2.320271e-02
> 0 Linear |R| = 2.320271e-02
> 1 Linear |R| = 4.367880e-03
> 2 Linear |R| = 1.407852e-03
> 3 Linear |R| = 6.036360e-04
> 4 Linear |R| = 1.867661e-04
> 5 Linear |R| = 8.760076e-05
> 6 Linear |R| = 3.260519e-05
> 7 Linear |R| = 1.435418e-05
> 8 Linear |R| = 4.532875e-06
> 9 Linear |R| = 2.439053e-06
> 10 Linear |R| = 7.998549e-07
> 11 Linear |R| = 2.428064e-07
> 12 Linear |R| = 4.766918e-08
> 13 Linear |R| = 1.713748e-08
> 2 Nonlinear |R| = 3.671573e-07
>
>
>
>
>
>
>
> >
> >
> > Fande,
> >
> >
> >
> >
> > On Wed, Nov 15, 2017 at 1:59 PM, Smith, Barry F. <bsmith at mcs.anl.gov> wrote:
> >
> > Meaningless differences
> >
> >
> > > On Nov 15, 2017, at 2:26 PM, Kong, Fande <fande.kong at inl.gov> wrote:
> > >
> > > Hi,
> > >
> > > There is a heat conduction problem. When superlu_dist is used as a preconditioner, we have random results from different runs. Is there a random algorithm in superlu_dist? If we use ASM or MUMPS as the preconditioner, we then don't have this issue.
> > >
> > > run 1:
> > >
> > > 0 Nonlinear |R| = 9.447423e+03
> > > 0 Linear |R| = 9.447423e+03
> > > 1 Linear |R| = 1.013384e-02
> > > 2 Linear |R| = 4.020995e-08
> > > 1 Nonlinear |R| = 1.404678e-02
> > > 0 Linear |R| = 1.404678e-02
> > > 1 Linear |R| = 5.104757e-08
> > > 2 Linear |R| = 7.699637e-14
> > > 2 Nonlinear |R| = 5.106418e-08
> > >
> > >
> > > run 2:
> > >
> > > 0 Nonlinear |R| = 9.447423e+03
> > > 0 Linear |R| = 9.447423e+03
> > > 1 Linear |R| = 1.013384e-02
> > > 2 Linear |R| = 4.020995e-08
> > > 1 Nonlinear |R| = 1.404678e-02
> > > 0 Linear |R| = 1.404678e-02
> > > 1 Linear |R| = 5.109913e-08
> > > 2 Linear |R| = 7.189091e-14
> > > 2 Nonlinear |R| = 5.111591e-08
> > >
> > > run 3:
> > >
> > > 0 Nonlinear |R| = 9.447423e+03
> > > 0 Linear |R| = 9.447423e+03
> > > 1 Linear |R| = 1.013384e-02
> > > 2 Linear |R| = 4.020995e-08
> > > 1 Nonlinear |R| = 1.404678e-02
> > > 0 Linear |R| = 1.404678e-02
> > > 1 Linear |R| = 5.104942e-08
> > > 2 Linear |R| = 7.465572e-14
> > > 2 Nonlinear |R| = 5.106642e-08
> > >
> > > run 4:
> > >
> > > 0 Nonlinear |R| = 9.447423e+03
> > > 0 Linear |R| = 9.447423e+03
> > > 1 Linear |R| = 1.013384e-02
> > > 2 Linear |R| = 4.020995e-08
> > > 1 Nonlinear |R| = 1.404678e-02
> > > 0 Linear |R| = 1.404678e-02
> > > 1 Linear |R| = 5.102730e-08
> > > 2 Linear |R| = 7.132220e-14
> > > 2 Nonlinear |R| = 5.104442e-08
> > >
> > > Solver details:
> > >
> > > SNES Object: 8 MPI processes
> > > type: newtonls
> > > maximum iterations=15, maximum function evaluations=10000
> > > tolerances: relative=1e-08, absolute=1e-11, solution=1e-50
> > > total number of linear solver iterations=4
> > > total number of function evaluations=7
> > > norm schedule ALWAYS
> > > SNESLineSearch Object: 8 MPI processes
> > > type: basic
> > > maxstep=1.000000e+08, minlambda=1.000000e-12
> > > tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08
> > > maximum iterations=40
> > > KSP Object: 8 MPI processes
> > > type: gmres
> > > restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
> > > happy breakdown tolerance 1e-30
> > > maximum iterations=100, initial guess is zero
> > > tolerances: relative=1e-06, absolute=1e-50, divergence=10000.
> > > right preconditioning
> > > using UNPRECONDITIONED norm type for convergence test
> > > PC Object: 8 MPI processes
> > > type: 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:
> > > Mat Object: 8 MPI processes
> > > type: superlu_dist
> > > rows=7925, cols=7925
> > > 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 4 x npcol 2
> > > Equilibrate matrix TRUE
> > > Matrix input mode 1
> > > Replace tiny pivots FALSE
> > > Use iterative refinement TRUE
> > > Processors in row 4 col partition 2
> > > Row permutation LargeDiag
> > > Column permutation METIS_AT_PLUS_A
> > > Parallel symbolic factorization FALSE
> > > Repeated factorization SamePattern
> > > linear system matrix followed by preconditioner matrix:
> > > Mat Object: 8 MPI processes
> > > type: mffd
> > > rows=7925, cols=7925
> > > Matrix-free approximation:
> > > err=1.49012e-08 (relative error in function evaluation)
> > > Using wp compute h routine
> > > Does not compute normU
> > > Mat Object: () 8 MPI processes
> > > type: mpiaij
> > > rows=7925, cols=7925
> > > total: nonzeros=63587, allocated nonzeros=63865
> > > total number of mallocs used during MatSetValues calls =0
> > > not using I-node (on process 0) routines
> > >
> > >
> > > Fande,
> > >
> > >
> >
> >
More information about the petsc-users
mailing list