[petsc-users] TS and snes_grid_sequence

[Francesco Magaletti]

Hi everyone,

I’m trying to solve a system of time dependent PDE’s, strongly non linear and quite stiff. The system is 1D, but I need a large number of grid points (1-10 million points). I’m facing some convergence problem of the Newton solver: if I use a small timestep (10^-5) the SNES converges correctly, but if I increase it, the Newton method diverges. Moreover, when I increase the number of grid points, the timestep for Newton convergence decreases. Such a restriction on the timestep is a big problem for my simulations.

I thought that the option -snes_grid_sequence could help the SNES to converge, but when I run the code the first grid converges and then the simulations abort with errors. Here is an example with 60000grid points:

mpiexec -n 4 ./code_petsc -ts_monitor -snes_monitor -snes_converged_reason -ksp_converged_reason -ftime 8.0 -ksp_rtol 1.0e-8 -snes_atol 1.0e-12 -snes_rtol 1.0e-14 -snes_stol 1.0e-12 -snes_max_it 2000 -dt 2.0e-4 -nx 60000 -snes_grid_sequence 1

0 TS dt 0.0002 time 0
      0 SNES Function norm 4.597340391780e+04 
      Linear solve converged due to CONVERGED_RTOL iterations 9
      1 SNES Function norm 3.986169680241e+03 
      Linear solve converged due to CONVERGED_RTOL iterations 14
      2 SNES Function norm 4.292840674611e+01 
      Linear solve converged due to CONVERGED_RTOL iterations 15
      3 SNES Function norm 1.044935520416e-02 
      Linear solve converged due to CONVERGED_RTOL iterations 14
      4 SNES Function norm 2.936744161136e-06 
      Linear solve converged due to CONVERGED_RTOL iterations 10
      5 SNES Function norm 4.471992600451e-08 
    Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 5
[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
[0]PETSC ERROR:   
[0]PETSC ERROR: Must call TSSetRHSFunction() and / or TSSetIFunction()
[0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.
[0]PETSC ERROR: Petsc Release Version 3.6.3, Dec, 03, 2015 
[0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++ --with-fc=gfortran --download-fblaslapack --download-mpich --download-mpich-device=ch3:nemesis
[0]PETSC ERROR: #1 TSComputeIFunction() line 723 in /home/magaletto/Scaricati/petsc-3.6.3/src/ts/interface/ts.c
[0]PETSC ERROR: #2 SNESTSFormFunction_Theta() line 483 in /home/magaletto/Scaricati/petsc-3.6.3/src/ts/impls/implicit/theta/theta.c
[0]PETSC ERROR: #3 SNESTSFormFunction() line 4138 in /home/magaletto/Scaricati/petsc-3.6.3/src/ts/interface/ts.c
[0]PETSC ERROR: #4 SNESComputeFunction() line 2067 in /home/magaletto/Scaricati/petsc-3.6.3/src/snes/interface/snes.c
[0]PETSC ERROR: #5 SNESSolve_NEWTONLS() line 184 in /home/magaletto/Scaricati/petsc-3.6.3/src/snes/impls/ls/ls.c
[0]PETSC ERROR: #6 SNESSolve() line 3906 in /home/magaletto/Scaricati/petsc-3.6.3/src/snes/interface/snes.c
[0]PETSC ERROR: #7 TSStep_Theta() line 198 in /home/magaletto/Scaricati/petsc-3.6.3/src/ts/impls/implicit/theta/theta.c
[0]PETSC ERROR: #8 TSStep() line 3101 in /home/magaletto/Scaricati/petsc-3.6.3/src/ts/interface/ts.c
[0]PETSC ERROR: #9 TSSolve() line 3285 in /home/magaletto/Scaricati/petsc-3.6.3/src/ts/interface/ts.c

===================================================================================
=   BAD TERMINATION OF ONE OF YOUR APPLICATION PROCESSES
=   EXIT CODE: 6


Where is the mistake? 
Could you suggest a "more convergent” SNES? Maybe a FAS as a nonlinear preconditioner? 

Hope someone can help here.
best regards

Francesco