[petsc-users] Problems with preconditioners, which one?
Filippo Spiga
filippo.spiga at disco.unimib.it
Tue Aug 3 07:27:21 CDT 2010
Dear all,
I'm not an expert so probably the answer of my problem is very easy
(I hope so!). I have a linear system (a distributed linear system) and I
want to solve it using SNES. I know the form of the solution (this is a
test case, then we want to apply the same method on another class of
problems). I already use part this code that works for another problem.
I only changed is the Jacobian and the Jacobian evaluation routine. I
tested the Jacobian using the option "-snes_type test" and the
differences between mine compared with the one calculated by PETSc is
"0" (*).
The matrix is very simple but is "singular" (determinant = 1.0519e-55)
and probably is also bad conditioned. At this point I tried the
preconditioners. ILU is not good because it doesn't work in a parallel
environment. HYPRE doesn't work, SNES diverges. I tried some basic
tuning of HYPRE without success. But I'm not an expert. So, what can I do?
I used this options (**) and SNES doesn't converge (***). Jacobian and
the Residual vector are (**). I also tried (without success) to change
rtol/atol, increasing the accurancy until 1.e-13. Any suggestion to try
to find a good preconditioner (and a good tuning of that preconditioner)
is really appreciate.
Thank you very much in advance!
Regards
(*)
Testing hand-coded Jacobian, if the ratio is,O(1.e-8), the hand-coded
Jacobian is probably correct.
(**)
-log_summary
-pc_type hypre
-snes_type ls
-snes_max_it 100000
-snes_rtol 1.e-8
-snes_atol 1.e-4
-snes_monitor
-snes_monitor_solution
-snes_monitor_true_residual true
-snes_monitor_solution_update
-snes_view
(***)
[0]: start=0, end=7
[1]: start=7, end=13
[2]: start=13, end=20
[3]: start=20, end=27
0 SNES Function norm 7.421625102155e-02
1 SNES Function norm 1.979632611100e-02
2 SNES Function norm 1.978787365526e-02
3 SNES Function norm 1.978784197958e-02
SNES Object:
type: ls
line search variant: SNESLineSearchCubic
alpha=0.0001, maxstep=1e+08, minlambda=1e-12
maximum iterations=100000, maximum function evaluations=10000
tolerances: relative=1e-08, absolute=0.0001, solution=1e-08
total number of linear solver iterations=9
total number of function evaluations=55
KSP Object:
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-05, absolute=1e-50, divergence=10000
left preconditioning
using PRECONDITIONED norm type for convergence test
PC Object:
type: hypre
HYPRE BoomerAMG preconditioning
HYPRE BoomerAMG: Cycle type V
HYPRE BoomerAMG: Maximum number of levels 25
HYPRE BoomerAMG: Maximum number of iterations PER hypre call 1
HYPRE BoomerAMG: Convergence tolerance PER hypre call 0
HYPRE BoomerAMG: Threshold for strong coupling 0.25
HYPRE BoomerAMG: Interpolation truncation factor 0
HYPRE BoomerAMG: Interpolation: max elements per row 0
HYPRE BoomerAMG: Number of levels of aggressive coarsening 0
HYPRE BoomerAMG: Number of paths for aggressive coarsening 1
HYPRE BoomerAMG: Maximum row sums 0.9
HYPRE BoomerAMG: Sweeps down 1
HYPRE BoomerAMG: Sweeps up 1
HYPRE BoomerAMG: Sweeps on coarse 1
HYPRE BoomerAMG: Relax down symmetric-SOR/Jacobi
HYPRE BoomerAMG: Relax up symmetric-SOR/Jacobi
HYPRE BoomerAMG: Relax on coarse Gaussian-elimination
HYPRE BoomerAMG: Relax weight (all) 1
HYPRE BoomerAMG: Outer relax weight (all) 1
HYPRE BoomerAMG: Using CF-relaxation
HYPRE BoomerAMG: Measure type local
HYPRE BoomerAMG: Coarsen type Falgout
HYPRE BoomerAMG: Interpolation type classical
linear system matrix = precond matrix:
Matrix Object:
type=mpiaij, rows=27, cols=27
total: nonzeros=223, allocated nonzeros=223
not using I-node (on process 0) routines
SNES Diverged. Reason LS_FAILURE
|residual|_2=1.978784e-02
|residualb|_inf=1.588862e-02
|Au-b|_2=1.978784e-02
|Au-b|_inf=1.588862e-02
(****) Jacobian is stored as Sparse matrix
Jacobian =
(1,1) 0.0185
(3,1) -0.0093
(4,1) -0.0093
(5,1) -0.0093
(26,1) -0.0278
(2,2) 0.0031
(5,2) -0.0093
(5,3) 0.0046
(7,3) -0.0046
(10,3) -0.0046
(13,3) -0.0139
(15,3) -0.0093
(26,3) -0.0093
(5,4) 0.0046
(6,4) -0.0139
(7,4) -0.0046
(16,4) -0.0093
(26,4) -0.0093
(27,4) -0.0046
(3,5) -0.0046
(4,5) -0.0046
(7,5) -0.0093
(26,5) -0.0093
(4,6) 0.0139
(6,6) 0.0139
(7,6) 0.0046
(16,6) 0.0093
(26,6) 0.0093
(27,6) 0.0046
(3,7) 0.0046
(4,7) 0.0046
(5,7) 0.0093
(7,7) 0.0093
(26,7) 0.0093
(3,8) -0.0046
(8,8) 0.0031
(10,8) -0.0046
(3,9) -0.0139
(5,9) -0.0046
(9,9) 0.0062
(3,10) 0.0046
(11,10) -0.0046
(13,10) -0.0046
(15,10) -0.0046
(10,11) 0.0046
(11,11) 0.0046
(13,11) 0.0046
(15,11) 0.0046
(6,12) 0.0093
(7,12) 0.0093
(12,12) 0.0278
(13,12) 0.0093
(14,12) 0.0093
(15,12) 0.0093
(16,12) 0.0093
(26,12) 0.0278
(3,13) 0.0139
(7,13) 0.0046
(10,13) 0.0046
(13,13) 0.0139
(15,13) 0.0093
(26,13) 0.0093
(12,14) -0.0093
(15,14) 0.0046
(16,14) 0.0046
(17,14) -0.0093
(18,14) -0.0046
(19,14) -0.0046
(26,14) 0.0093
(3,15) 0.0093
(10,15) 0.0046
(11,15) -0.0046
(12,15) -0.0093
(13,15) -0.0093
(14,15) -0.0046
(18,15) -0.0139
(26,15) 0.0093
(4,16) 0.0093
(6,16) -0.0093
(12,16) -0.0093
(14,16) -0.0046
(19,16) -0.0139
(20,16) -0.0046
(26,16) 0.0093
(27,16) 0.0046
(12,17) 0.0093
(14,17) 0.0093
(17,17) 0.0093
(18,17) 0.0046
(19,17) 0.0046
(11,18) 0.0046
(12,18) 0.0093
(13,18) 0.0093
(14,18) 0.0046
(15,18) 0.0139
(18,18) 0.0139
(6,19) 0.0093
(12,19) 0.0093
(14,19) 0.0046
(16,19) 0.0139
(19,19) 0.0139
(20,19) 0.0046
(6,20) 0.0046
(16,20) 0.0046
(20,20) 0.0046
(27,20) 0.0046
(14,21) -0.0093
(15,21) -0.0046
(16,21) -0.0046
(21,21) 0.0093
(26,21) -0.0093
(3,22) -0.0093
(10,22) -0.0046
(15,22) -0.0139
(22,22) 0.0123
(26,22) -0.0093
(4,23) -0.0093
(16,23) -0.0139
(23,23) 0.0123
(26,23) -0.0093
(27,23) -0.0046
(4,24) -0.0046
(24,24) 0.0031
(27,24) -0.0046
(4,25) -0.0139
(5,25) -0.0046
(25,25) 0.0062
(3,26) 0.0093
(4,26) 0.0093
(5,26) 0.0093
(6,26) -0.0093
(7,26) -0.0093
(12,26) -0.0278
(13,26) -0.0093
(14,26) -0.0093
(15,26) -0.0093
(16,26) -0.0093
(26,26) -0.0000
(4,27) 0.0046
(6,27) -0.0046
(16,27) -0.0046
(20,27) -0.0046
Residual =
0
0
0.0001
-0.0101
0.0001
-0.0001
-0.0001
0
0
0.0000
0.0000
-0.0004
-0.0001
-0.0001
-0.0040
-0.0040
0.0000
0.0000
0.0000
0.0000
0
0
0
0
0
-0.0159
-0.0021
--
===============================================================
Filippo SPIGA MSc, HPC and GRID Technologist
tel.: +39 340 8387735 skype: filippo.spiga
===============================================================
«Nobody will drive us out of Cantor's paradise.»
-- David Hilbert
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