[petsc-dev] Multigrid is confusing

[Jed Brown]

If ex19 is what matters...

$ base='mpiexec.hydra -n 4 ./ex19 -da_refine 3 -lidvelocity 100 -grashof
1e4 -pc_type mg -ksp_type fgmres -pc_mg_type full -ksp_converged_reason'
$ $base
lid velocity = 100, prandtl # = 1, grashof # = 10000
  Linear solve converged due to CONVERGED_RTOL iterations 23
  Linear solve converged due to CONVERGED_RTOL iterations 12
  Linear solve converged due to CONVERGED_RTOL iterations 12
  Linear solve converged due to CONVERGED_RTOL iterations 17
  Linear solve converged due to CONVERGED_RTOL iterations 15
  Linear solve converged due to CONVERGED_RTOL iterations 13
  Linear solve converged due to CONVERGED_RTOL iterations 19
  Linear solve converged due to CONVERGED_RTOL iterations 21
  Linear solve converged due to CONVERGED_RTOL iterations 18
Number of SNES iterations = 9
$ $base -mg_levels_ksp_type chebyshev
-mg_levels_ksp_chebyshev_estimate_eigenvalues 0.1,1.1 -mg_levels_ksp_max_it
1 -mg_levels_pc_type pbjacobi
lid velocity = 100, prandtl # = 1, grashof # = 10000
  Linear solve converged due to CONVERGED_RTOL iterations 25
  Linear solve converged due to CONVERGED_RTOL iterations 27
  Linear solve converged due to CONVERGED_RTOL iterations 27
  Linear solve converged due to CONVERGED_RTOL iterations 30
  Linear solve converged due to CONVERGED_RTOL iterations 28
  Linear solve converged due to CONVERGED_RTOL iterations 42
  Linear solve converged due to CONVERGED_RTOL iterations 49
  Linear solve converged due to CONVERGED_RTOL iterations 52
  Linear solve converged due to CONVERGED_RTOL iterations 48
Number of SNES iterations = 9
$ $base -mg_levels_ksp_type chebyshev
-mg_levels_ksp_chebyshev_estimate_eigenvalues 0.1,1.1 -mg_levels_ksp_max_it
1 -mg_levels_pc_type sor
lid velocity = 100, prandtl # = 1, grashof # = 10000
  Linear solve converged due to CONVERGED_RTOL iterations 22
  Linear solve converged due to CONVERGED_RTOL iterations 16
  Linear solve converged due to CONVERGED_RTOL iterations 17
  Linear solve converged due to CONVERGED_RTOL iterations 19
  Linear solve converged due to CONVERGED_RTOL iterations 19
  Linear solve converged due to CONVERGED_RTOL iterations 17
  Linear solve converged due to CONVERGED_RTOL iterations 20
  Linear solve converged due to CONVERGED_RTOL iterations 18
  Linear solve converged due to CONVERGED_RTOL iterations 17
Number of SNES iterations = 9
$ $base -mg_levels_ksp_type chebyshev
-mg_levels_ksp_chebyshev_estimate_eigenvalues 0.1,1.1 -mg_levels_ksp_max_it
2 -mg_levels_pc_type pbjacobi
lid velocity = 100, prandtl # = 1, grashof # = 10000
  Linear solve converged due to CONVERGED_RTOL iterations 15
  Linear solve converged due to CONVERGED_RTOL iterations 13
  Linear solve converged due to CONVERGED_RTOL iterations 16
  Linear solve converged due to CONVERGED_RTOL iterations 15
  Linear solve converged due to CONVERGED_RTOL iterations 16
  Linear solve converged due to CONVERGED_RTOL iterations 16
  Linear solve converged due to CONVERGED_RTOL iterations 18
  Linear solve converged due to CONVERGED_RTOL iterations 17
  Linear solve converged due to CONVERGED_RTOL iterations 16
Number of SNES iterations = 9
$ $base -mg_levels_ksp_type chebyshev
-mg_levels_ksp_chebyshev_estimate_eigenvalues 0.1,1.1 -mg_levels_ksp_max_it
2 -mg_levels_pc_type sor
lid velocity = 100, prandtl # = 1, grashof # = 10000
  Linear solve converged due to CONVERGED_RTOL iterations 10
  Linear solve converged due to CONVERGED_RTOL iterations 7
  Linear solve converged due to CONVERGED_RTOL iterations 8
  Linear solve converged due to CONVERGED_RTOL iterations 8
  Linear solve converged due to CONVERGED_RTOL iterations 9
  Linear solve converged due to CONVERGED_RTOL iterations 9
  Linear solve converged due to CONVERGED_RTOL iterations 8
  Linear solve converged due to CONVERGED_RTOL iterations 8
  Linear solve converged due to CONVERGED_RTOL iterations 7
Number of SNES iterations = 9
$ $base -mg_levels_ksp_type chebyshev
-mg_levels_ksp_chebyshev_estimate_eigenvalues 0.1,1.1 -mg_levels_ksp_max_it
3 -mg_levels_pc_type pbjacobi
lid velocity = 100, prandtl # = 1, grashof # = 10000
  Linear solve converged due to CONVERGED_RTOL iterations 12
  Linear solve converged due to CONVERGED_RTOL iterations 9
  Linear solve converged due to CONVERGED_RTOL iterations 11
  Linear solve converged due to CONVERGED_RTOL iterations 11
  Linear solve converged due to CONVERGED_RTOL iterations 11
  Linear solve converged due to CONVERGED_RTOL iterations 12
  Linear solve converged due to CONVERGED_RTOL iterations 12
  Linear solve converged due to CONVERGED_RTOL iterations 11
  Linear solve converged due to CONVERGED_RTOL iterations 11
Number of SNES iterations = 9
$ $base -mg_levels_ksp_type chebyshev
-mg_levels_ksp_chebyshev_estimate_eigenvalues 0.1,1.1 -mg_levels_ksp_max_it
3 -mg_levels_pc_type sor
lid velocity = 100, prandtl # = 1, grashof # = 10000
  Linear solve converged due to CONVERGED_RTOL iterations 9
  Linear solve converged due to CONVERGED_RTOL iterations 6
  Linear solve converged due to CONVERGED_RTOL iterations 6
  Linear solve converged due to CONVERGED_RTOL iterations 7
  Linear solve converged due to CONVERGED_RTOL iterations 7
  Linear solve converged due to CONVERGED_RTOL iterations 6
  Linear solve converged due to CONVERGED_RTOL iterations 7
  Linear solve converged due to CONVERGED_RTOL iterations 6
  Linear solve converged due to CONVERGED_RTOL iterations 6
Number of SNES iterations = 9
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