Hi,
I am successfully using PETSc (v3.4.2) to solve a 3D Poisson's equation
with CG + GAMG as I was suggested to do in a previous thread.
So far I am using GAMG with the default settings, i.e.
-pc_type gamg -pc_gamg_agg_nsmooths 1
The speed of the solution is satisfactory, but I would like to know if
you have any suggestions to further speed it up, particularly
if there is any parameters worth looking into to achieve an even faster
solution, for example number of levels and so on.
So far I am using Dirichlet's BCs for my test case, but I will soon have
periodic conditions: in this case, does GAMG require particular settings?
Finally, I did not try geometric multigrid: do you think it is worth a shot?
Here are my current settings:
I run with
-pc_type gamg -pc_gamg_agg_nsmooths 1 -ksp_view -options_left
and the output is:
KSP Object: 4 MPI processes
type: cg
maximum iterations=10000
tolerances: relative=1e-08, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using UNPRECONDITIONED norm type for convergence test
PC Object: 4 MPI processes
type: gamg
MG: type is MULTIPLICATIVE, levels=3 cycles=v
Cycles per PCApply=1
Using Galerkin computed coarse grid matrices
Coarse grid solver -- level -------------------------------
KSP Object: (mg_coarse_) 4 MPI processes
type: preonly
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (mg_coarse_) 4 MPI processes
type: bjacobi
block Jacobi: number of blocks = 4
Local solve info for each block is in the following KSP and PC
objects:
[0] number of local blocks = 1, first local block number = 0
[0] local block number 0
KSP Object: (mg_coarse_sub_) 1 MPI processes
type: preonly
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50,
divergence=10000
KSP Object: (mg_coarse_sub_) left preconditioning
using NONE norm type for convergence test
PC Object: (mg_coarse_sub_) 1 MPI processes
type: preonly
1 MPI processes
type: lu
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
LU: out-of-place factorization
left preconditioning
using NONE norm type for convergence test
PC Object: (mg_coarse_sub_) 1 MPI processes
type: lu
tolerance for zero pivot 2.22045e-14
using diagonal shift on blocks to prevent zero pivot
matrix ordering: nd
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-14
using diagonal shift on blocks to prevent zero pivot
matrix ordering: nd
factor fill ratio given 5, needed 0
Factored matrix follows:
factor fill ratio given 5, needed 4.13207
Factored matrix follows:
Matrix Object: Matrix
Object: 1 MPI processes
type: seqaij
rows=395, cols=395
package used to perform factorization: petsc
total: nonzeros=132379, allocated nonzeros=132379
total number of mallocs used during MatSetValues calls =0
not using I-node routines
1 MPI processes
type: seqaij
linear system matrix = precond matrix:
rows=0, cols=0
package used to perform factorization: petsc
total: nonzeros=1, allocated nonzeros=1
total number of mallocs used during MatSetValues
calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
Matrix Object:KSP Object: 1 MPI processes
type: seqaij
rows=0, cols=0
total: nonzeros=0, allocated nonzeros=0
total number of mallocs used during MatSetValues calls =0
not using I-node routines
rows=395, cols=395
total: nonzeros=32037, allocated nonzeros=32037
total number of mallocs used during MatSetValues calls =0
not using I-node routines
- - - - - - - - - - - - - - - - - -
KSP Object: (mg_coarse_sub_) 1 MPI processes
type: preonly
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (mg_coarse_sub_) 1 MPI processes
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-14
using diagonal shift on blocks to prevent zero pivot
matrix ordering: nd
factor fill ratio given 5, needed 0
Factored matrix follows:
Matrix Object: 1 MPI processes
type: seqaij
rows=0, cols=0
package used to perform factorization: petsc
total: nonzeros=1, allocated nonzeros=1
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=0, cols=0
total: nonzeros=0, allocated nonzeros=0
total number of mallocs used during MatSetValues calls =0
not using I-node routines
(mg_coarse_sub_) 1 MPI processes
type: preonly
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (mg_coarse_sub_) 1 MPI processes
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-14
using diagonal shift on blocks to prevent zero pivot
matrix ordering: nd
factor fill ratio given 5, needed 0
Factored matrix follows:
Matrix Object: 1 MPI processes
type: seqaij
rows=0, cols=0
package used to perform factorization: petsc
total: nonzeros=1, allocated nonzeros=1
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=0, cols=0
total: nonzeros=0, allocated nonzeros=0
total number of mallocs used during MatSetValues calls =0
not using I-node routines
[1] number of local blocks = 1, first local block number = 1
[1] local block number 0
- - - - - - - - - - - - - - - - - -
[2] number of local blocks = 1, first local block number = 2
[2] local block number 0
- - - - - - - - - - - - - - - - - -
[3] number of local blocks = 1, first local block number = 3
[3] local block number 0
- - - - - - - - - - - - - - - - - -
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=395, cols=395
total: nonzeros=32037, allocated nonzeros=32037
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
Down solver (pre-smoother) on level 1 -------------------------------
KSP Object: (mg_levels_1_) 4 MPI processes
type: chebyshev
Chebyshev: eigenvalue estimates: min = 0.0636225, max = 1.33607
maximum iterations=2
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using NONE norm type for convergence test
PC Object: (mg_levels_1_) 4 MPI processes
type: jacobi
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=23918, cols=23918
total: nonzeros=818732, allocated nonzeros=818732
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
Up solver (post-smoother) same as down solver (pre-smoother)
Down solver (pre-smoother) on level 2 -------------------------------
KSP Object: (mg_levels_2_) 4 MPI processes
type: chebyshev
Chebyshev: eigenvalue estimates: min = 0.0971369, max = 2.03987
maximum iterations=2
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using NONE norm type for convergence test
PC Object: (mg_levels_2_) 4 MPI processes
type: jacobi
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=262144, cols=262144
total: nonzeros=1835008, allocated nonzeros=1835008
total number of mallocs used during MatSetValues calls =0
Up solver (post-smoother) same as down solver (pre-smoother)
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=262144, cols=262144
total: nonzeros=1835008, allocated nonzeros=1835008
total number of mallocs used during MatSetValues calls =0
#PETSc Option Table entries:
-ksp_view
-options_left
-pc_gamg_agg_nsmooths 1
-pc_type gamg
#End of PETSc Option Table entries
There are no unused options.
Thank you,
Michele
