# [petsc-users] superlu_dist produces random results

Smith, Barry F. bsmith at mcs.anl.gov
Wed Nov 15 17:04:49 CST 2017

```  Do the ASM runs for thousands of time-steps produce the same final "physical results" as the MUMPS run for thousands of timesteps?  While with SuperLU you get a very different "physical results"?

Barry

> On Nov 15, 2017, at 4:52 PM, Kong, Fande <fande.kong at inl.gov> wrote:
>
>
>
> On Wed, Nov 15, 2017 at 3:35 PM, Smith, Barry F. <bsmith at mcs.anl.gov> wrote:
>
>   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?
>
> We are using Jacobian-free Newton. So Jacobian is different from the preconditioning matrix.
>
>
>    What happens if you do no lagging and solve each linear solve with a new LU factorization?
>
> We have the following results without using Jacobian-free Newton. Again, superlu_dist produces differences, while MUMPS gives the same results in terms of the residual norms.
>
>
> Fande,
>
>
> Superlu_dist run1:
>
>  0 Nonlinear |R| = 9.447423e+03
>       0 Linear |R| = 9.447423e+03
>       1 Linear |R| = 1.322285e-11
>  1 Nonlinear |R| = 1.666987e-11
>
>
> Superlu_dist run2:
>
>  0 Nonlinear |R| = 9.447423e+03
>       0 Linear |R| = 9.447423e+03
>       1 Linear |R| = 1.322171e-11
>  1 Nonlinear |R| = 1.666977e-11
>
>
> Superlu_dist run3:
>
>  0 Nonlinear |R| = 9.447423e+03
>       0 Linear |R| = 9.447423e+03
>       1 Linear |R| = 1.321964e-11
>  1 Nonlinear |R| = 1.666959e-11
>
>
> Superlu_dist run4:
>
>  0 Nonlinear |R| = 9.447423e+03
>       0 Linear |R| = 9.447423e+03
>       1 Linear |R| = 1.321978e-11
>  1 Nonlinear |R| = 1.668688e-11
>
>
> MUMPS run1:
>
>  0 Nonlinear |R| = 9.447423e+03
>       0 Linear |R| = 9.447423e+03
>       1 Linear |R| = 1.360637e-11
>  1 Nonlinear |R| = 1.654334e-11
>
> MUMPS run 2:
>
>  0 Nonlinear |R| = 9.447423e+03
>       0 Linear |R| = 9.447423e+03
>       1 Linear |R| = 1.360637e-11
>  1 Nonlinear |R| = 1.654334e-11
>
> MUMPS run 3:
>
>  0 Nonlinear |R| = 9.447423e+03
>       0 Linear |R| = 9.447423e+03
>       1 Linear |R| = 1.360637e-11
>  1 Nonlinear |R| = 1.654334e-11
>
> MUMPS run4:
>
>  0 Nonlinear |R| = 9.447423e+03
>       0 Linear |R| = 9.447423e+03
>       1 Linear |R| = 1.360637e-11
>  1 Nonlinear |R| = 1.654334e-11
>
>
>
>
>
>
>
>
>
>   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,
> > > >
> > > >
> > >
> > >
>
>

```