[petsc-users] Any changes in ML usage between 3.1-p8 -> 3.3-p6?
Jozsef Bakosi
jbakosi at lanl.gov
Wed Apr 17 17:21:03 CDT 2013
> On 04.17.2013 15:38, Matthew Knepley wrote:
>
> > On 04.17.2013 14:26, Jozsef Bakosi wrote:
> >
> > > Mark F. Adams mark.adams at columbia.edu
> > > Wed Apr 17 14:25:04 CDT 2013
> > >
> > > 2) If you get "Indefinite PC" (I am guessing from using CG) it is because the
> > > preconditioner
> > > really is indefinite (or possible non-symmetric). We improved the checking
> > > for this in one
> > > of those releases.
> > >
> > > AMG does not guarantee an SPD preconditioner so why persist in trying to use
> > > CG?
> > >
> > >
> > > AMG is positive if everything is working correctly.
> > >
> > > Are these problems only semidefinite? Singular systems can give erratic
> > > behavior.
> >
> > It is a Laplace operator from Galerkin finite elements. And the PC is fine on
> > ranks 1, 2, 3, and 5 -- indefinite only on 4. I think we can safely say that the
> > same PC should be positive on 4 as well.
>
> Why is it safe? Because it sounds plausible? Mathematics is replete with things
> that sound plausible and are false. Are there proofs that suggest this? Is there
> computational evidence? Why would I believe you?
Okay, so here is some additional information:
I tried both old and new PETSc versions again, but now only taking 2 iterations
(both with 4 CPUs) and checked the residuals. I get the same exact PC from ML in
both cases, however, the residuals are different after both iterations:
Please do a diff on the attached files and you can verify that the ML
diagnostics are exactly the same: same max eigenvalues, nodes aggregated, etc,
while the norm coming out of the solver at the end at both iterations are
different.
We reproduced the same exact behavior on two different linux platforms.
Once again: same application source code, same ML source code, different PETSc:
3.1-p8 vs. 3.3-p6.
-------------- next part --------------
Entering ML_Gen_MGHierarchy_UsingAggregation
**************************************************************
* ML Aggregation information *
==============================================================
ML_Aggregate : ordering = natural.
ML_Aggregate : min nodes/aggr = 2
ML_Aggregate : max neigh selected = 0
ML_Aggregate : attach scheme = MAXLINK
ML_Aggregate : strong threshold = 0.000000e+00
ML_Aggregate : P damping factor = 1.333333e+00
ML_Aggregate : number of PDEs = 1
ML_Aggregate : number of null vec = 1
ML_Aggregate : smoother drop tol = 0.000000e+00
ML_Aggregate : max coarse size = 250
ML_Aggregate : max no. of levels = 10
**************************************************************
ML_Aggregate_Coarsen (level 0) begins
ML_Aggregate_CoarsenUncoupled : current level = 0
ML_Aggregate_CoarsenUncoupled : current eps = 0.000000e+00
Aggregation(UVB) : Total nonzeros = 6183334 (Nrows=236600)
Aggregation(UC) : Phase 0 - no. of bdry pts = 0
Aggregation(UC) : Phase 1 - nodes aggregated = 216030 (236600)
Aggregation(UC) : Phase 1 - total aggregates = 9124
Aggregation(UC_Phase2_3) : Phase 1 - nodes aggregated = 216030
Aggregation(UC_Phase2_3) : Phase 1 - total aggregates = 9124
Aggregation(UC_Phase2_3) : Phase 2a- additional aggregates = 0
Aggregation(UC_Phase2_3) : Phase 2 - total aggregates = 9124
Aggregation(UC_Phase2_3) : Phase 2 - boundary nodes = 0
Aggregation(UC_Phase2_3) : Phase 3 - leftovers = 0 and singletons = 0
Gen_Prolongator (level 0) : Max eigenvalue = 4.2404e+00
Prolongator/Restriction smoother (level 0) : damping factor #1 = 3.1444e-01
Prolongator/Restriction smoother (level 0) : ( = 1.3333e+00 / 4.2404e+00)
ML_Aggregate_Coarsen (level 1) begins
ML_Aggregate_CoarsenUncoupled : current level = 1
ML_Aggregate_CoarsenUncoupled : current eps = 0.000000e+00
Aggregation(UVB) : Total nonzeros = 267508 (Nrows=9124)
Aggregation(UC) : Phase 0 - no. of bdry pts = 0
Aggregation(UC) : Phase 1 - nodes aggregated = 5944 (9124)
Aggregation(UC) : Phase 1 - total aggregates = 293
Aggregation(UC_Phase2_3) : Phase 1 - nodes aggregated = 5944
Aggregation(UC_Phase2_3) : Phase 1 - total aggregates = 293
Aggregation(UC_Phase2_3) : Phase 2a- additional aggregates = 45
Aggregation(UC_Phase2_3) : Phase 2 - total aggregates = 338
Aggregation(UC_Phase2_3) : Phase 2 - boundary nodes = 0
Aggregation(UC_Phase2_3) : Phase 3 - leftovers = 0 and singletons = 0
Gen_Prolongator (level 1) : Max eigenvalue = 1.9726e+00
Prolongator/Restriction smoother (level 1) : damping factor #1 = 6.7594e-01
Prolongator/Restriction smoother (level 1) : ( = 1.3333e+00 / 1.9726e+00)
ML_Aggregate_Coarsen (level 2) begins
ML_Aggregate_CoarsenUncoupled : current level = 2
ML_Aggregate_CoarsenUncoupled : current eps = 0.000000e+00
Aggregation(UVB) : Total nonzeros = 12942 (Nrows=338)
Aggregation(UC) : Phase 0 - no. of bdry pts = 0
Aggregation(UC) : Phase 1 - nodes aggregated = 174 (338)
Aggregation(UC) : Phase 1 - total aggregates = 10
Aggregation(UC_Phase2_3) : Phase 1 - nodes aggregated = 174
Aggregation(UC_Phase2_3) : Phase 1 - total aggregates = 10
Aggregation(UC_Phase2_3) : Phase 2a- additional aggregates = 5
Aggregation(UC_Phase2_3) : Phase 2 - total aggregates = 15
Aggregation(UC_Phase2_3) : Phase 2 - boundary nodes = 0
Aggregation(UC_Phase2_3) : Phase 3 - leftovers = 0 and singletons = 0
Gen_Prolongator (level 2) : Max eigenvalue = 1.4886e+00
Prolongator/Restriction smoother (level 2) : damping factor #1 = 8.9569e-01
Prolongator/Restriction smoother (level 2) : ( = 1.3333e+00 / 1.4886e+00)
Smoothed Aggregation : operator complexity = 1.045392e+00.
KSP Object:(PPE_)
type: cg
maximum iterations=10000
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using UNPRECONDITIONED norm type for convergence test
PC Object:(PPE_)
type: ml
MG: type is MULTIPLICATIVE, levels=4 cycles=v
Cycles per PCApply=1
Coarse grid solver -- level 0 presmooths=1 postsmooths=1 -----
KSP Object:(PPE_mg_coarse_)
type: preonly
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using PRECONDITIONED norm type for convergence test
PC Object:(PPE_mg_coarse_)
type: redundant
Redundant preconditioner: First (color=0) of 4 PCs follows
KSP Object:(PPE_mg_coarse_redundant_)
type: preonly
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:(PPE_mg_coarse_redundant_)
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-16
matrix ordering: nd
factor fill ratio given 5, needed 1
Factored matrix follows:
Matrix Object:
type=seqaij, rows=15, cols=15
package used to perform factorization: petsc
total: nonzeros=225, allocated nonzeros=225
using I-node routines: found 3 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object:
type=seqaij, rows=15, cols=15
total: nonzeros=225, allocated nonzeros=225
using I-node routines: found 3 nodes, limit used is 5
KSP Object:(PPE_mg_coarse_redundant_)
type: preonly
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:(PPE_mg_coarse_redundant_)
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-16
matrix ordering: nd
factor fill ratio given 5, needed 1
Factored matrix follows:
Matrix Object:
type=seqaij, rows=15, cols=15
package used to perform factorization: petsc
total: nonzeros=225, allocated nonzeros=225
using I-node routines: found 3 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object:
type=seqaij, rows=15, cols=15
total: nonzeros=225, allocated nonzeros=225
using I-node routines: found 3 nodes, limit used is 5
KSP Object:(PPE_mg_coarse_redundant_)
type: preonly
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:(PPE_mg_coarse_redundant_)
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-16
matrix ordering: nd
factor fill ratio given 5, needed 1
Factored matrix follows:
Matrix Object:
type=seqaij, rows=15, cols=15
package used to perform factorization: petsc
total: nonzeros=225, allocated nonzeros=225
using I-node routines: found 3 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object:
type=seqaij, rows=15, cols=15
total: nonzeros=225, allocated nonzeros=225
using I-node routines: found 3 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object:
type=mpiaij, rows=15, cols=15
total: nonzeros=225, allocated nonzeros=225
using I-node (on process 0) routines: found 1 nodes, limit used is 5
Down solver (pre-smoother) on level 1 smooths=1 --------------------
KSP Object:(PPE_mg_levels_1_)
type: richardson
Richardson: damping factor=0.9
maximum iterations=1
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using NO norm type for convergence test
PC Object:(PPE_mg_levels_1_)
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object:(PPE_mg_levels_1_sub_)
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NO norm type for convergence test
PC Object:(PPE_mg_levels_1_sub_)
type: icc
0 levels of fill
tolerance for zero pivot 1e-12
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object:
type=seqaij, rows=81, cols=81
total: nonzeros=2091, allocated nonzeros=2091
not using I-node routines
linear system matrix = precond matrix:
Matrix Object:
type=mpiaij, rows=338, cols=338
total: nonzeros=12942, allocated nonzeros=12942
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 smooths=1 --------------------
KSP Object:(PPE_mg_levels_2_)
type: richardson
Richardson: damping factor=0.9
maximum iterations=1
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using NO norm type for convergence test
PC Object:(PPE_mg_levels_2_)
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object:(PPE_mg_levels_2_sub_)
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NO norm type for convergence test
PC Object:(PPE_mg_levels_2_sub_)
type: icc
0 levels of fill
tolerance for zero pivot 1e-12
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object:
type=seqaij, rows=2265, cols=2265
total: nonzeros=60131, allocated nonzeros=60131
not using I-node routines
linear system matrix = precond matrix:
Matrix Object:
type=mpiaij, rows=9124, cols=9124
total: nonzeros=267508, allocated nonzeros=267508
not using I-node (on process 0) routines
Up solver (post-smoother) same as down solver (pre-smoother)
Down solver (pre-smoother) on level 3 smooths=1 --------------------
KSP Object:(PPE_mg_levels_3_)
type: richardson
Richardson: damping factor=0.9
maximum iterations=1
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using NO norm type for convergence test
PC Object:(PPE_mg_levels_3_)
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object:(PPE_mg_levels_3_sub_)
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NO norm type for convergence test
PC Object:(PPE_mg_levels_3_sub_)
type: icc
0 levels of fill
tolerance for zero pivot 1e-12
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object:
type=seqaij, rows=59045, cols=59045
total: nonzeros=1504413, allocated nonzeros=1594215
not using I-node routines
linear system matrix = precond matrix:
Matrix Object:
type=mpiaij, rows=236600, cols=236600
total: nonzeros=6183334, allocated nonzeros=12776400
not using I-node (on process 0) routines
Up solver (post-smoother) same as down solver (pre-smoother)
linear system matrix = precond matrix:
Matrix Object:
type=mpiaij, rows=236600, cols=236600
total: nonzeros=6183334, allocated nonzeros=12776400
not using I-node (on process 0) routines
solver: ||b|| = 5.9221e-03
solver: ||x(0)|| = 0.0000e+00
solver: Iteration: 1 ||r|| = 3.7007e-03 ||x(i+1)-x(i)|| = 1.2896e+01 ||x(i+1)|| = 1.2896e+01
solver: Iteration: 2 ||r|| = 2.8927e-03 ||x(i+1)-x(i)|| = 2.8520e+00 ||x(i+1)|| = 1.2444e+01
-------------- next part --------------
ML_Gen_MultiLevelHierarchy (level 0) : Gen Restriction and Prolongator
ML_Aggregate_Coarsen (level 0) begins
ML_Aggregate_CoarsenUncoupled : current level = 0
ML_Aggregate_CoarsenUncoupled : current eps = 0.000000e+00
Aggregation(UVB) : Total nonzeros = 6183334 (Nrows=236600)
Aggregation(UC) : Phase 0 - no. of bdry pts = 0
Aggregation(UC) : Phase 1 - nodes aggregated = 216030 (236600)
Aggregation(UC) : Phase 1 - total aggregates = 9124
Aggregation(UC_Phase2_3) : Phase 1 - nodes aggregated = 216030
Aggregation(UC_Phase2_3) : Phase 1 - total aggregates = 9124
Aggregation(UC_Phase2_3) : Phase 2a- additional aggregates = 0
Aggregation(UC_Phase2_3) : Phase 2 - total aggregates = 9124
Aggregation(UC_Phase2_3) : Phase 2 - boundary nodes = 0
Aggregation(UC_Phase2_3) : Phase 3 - leftovers = 0 and singletons = 0
Gen_Prolongator (level 0) : Max eigenvalue = 4.2404e+00
Prolongator/Restriction smoother (level 0) : damping factor #1 = 3.1444e-01
Prolongator/Restriction smoother (level 0) : ( = 1.3333e+00 / 4.2404e+00)
ML_Gen_MultiLevelHierarchy (level 1) : Gen Restriction and Prolongator
ML_Aggregate_Coarsen (level 1) begins
ML_Aggregate_CoarsenUncoupled : current level = 1
ML_Aggregate_CoarsenUncoupled : current eps = 0.000000e+00
Aggregation(UVB) : Total nonzeros = 267508 (Nrows=9124)
Aggregation(UC) : Phase 0 - no. of bdry pts = 0
Aggregation(UC) : Phase 1 - nodes aggregated = 5944 (9124)
Aggregation(UC) : Phase 1 - total aggregates = 293
Aggregation(UC_Phase2_3) : Phase 1 - nodes aggregated = 5944
Aggregation(UC_Phase2_3) : Phase 1 - total aggregates = 293
Aggregation(UC_Phase2_3) : Phase 2a- additional aggregates = 45
Aggregation(UC_Phase2_3) : Phase 2 - total aggregates = 338
Aggregation(UC_Phase2_3) : Phase 2 - boundary nodes = 0
Aggregation(UC_Phase2_3) : Phase 3 - leftovers = 0 and singletons = 0
Gen_Prolongator (level 1) : Max eigenvalue = 1.9726e+00
Prolongator/Restriction smoother (level 1) : damping factor #1 = 6.7594e-01
Prolongator/Restriction smoother (level 1) : ( = 1.3333e+00 / 1.9726e+00)
ML_Gen_MultiLevelHierarchy (level 2) : Gen Restriction and Prolongator
ML_Aggregate_Coarsen (level 2) begins
ML_Aggregate_CoarsenUncoupled : current level = 2
ML_Aggregate_CoarsenUncoupled : current eps = 0.000000e+00
Aggregation(UVB) : Total nonzeros = 12942 (Nrows=338)
Aggregation(UC) : Phase 0 - no. of bdry pts = 0
Aggregation(UC) : Phase 1 - nodes aggregated = 174 (338)
Aggregation(UC) : Phase 1 - total aggregates = 10
Aggregation(UC_Phase2_3) : Phase 1 - nodes aggregated = 174
Aggregation(UC_Phase2_3) : Phase 1 - total aggregates = 10
Aggregation(UC_Phase2_3) : Phase 2a- additional aggregates = 5
Aggregation(UC_Phase2_3) : Phase 2 - total aggregates = 15
Aggregation(UC_Phase2_3) : Phase 2 - boundary nodes = 0
Aggregation(UC_Phase2_3) : Phase 3 - leftovers = 0 and singletons = 0
Gen_Prolongator (level 2) : Max eigenvalue = 1.4886e+00
Prolongator/Restriction smoother (level 2) : damping factor #1 = 8.9569e-01
Prolongator/Restriction smoother (level 2) : ( = 1.3333e+00 / 1.4886e+00)
Smoothed Aggregation : operator complexity = 1.045392e+00.
KSP Object:(PPE_) 4 MPI processes
type: cg
maximum iterations=10000
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using UNPRECONDITIONED norm type for convergence test
PC Object:(PPE_) 4 MPI processes
type: ml
MG: type is MULTIPLICATIVE, levels=4 cycles=v
Cycles per PCApply=1
Using Galerkin computed coarse grid matrices
Coarse grid solver -- level -------------------------------
KSP Object: (PPE_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: (PPE_mg_coarse_) 4 MPI processes
type: redundant
Redundant preconditioner: First (color=0) of 4 PCs follows
KSP Object: (PPE_mg_coarse_redundant_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (PPE_mg_coarse_redundant_) 1 MPI processes
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-16
matrix ordering: nd
factor fill ratio given 5, needed 1
Factored matrix follows:
Matrix Object: 1 MPI processes
type: seqaij
rows=15, cols=15
package used to perform factorization: petsc
total: nonzeros=225, allocated nonzeros=225
total number of mallocs used during MatSetValues calls =0
using I-node routines: found 3 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=15, cols=15
total: nonzeros=225, allocated nonzeros=225
total number of mallocs used during MatSetValues calls =0
using I-node routines: found 3 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=15, cols=15
total: nonzeros=225, allocated nonzeros=225
total number of mallocs used during MatSetValues calls =0
using I-node (on process 0) routines: found 1 nodes, limit used is 5
Down solver (pre-smoother) on level 1 -------------------------------
KSP Object: (PPE_mg_levels_1_) 4 MPI processes
type: richardson
Richardson: damping factor=0.9
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: (PPE_mg_levels_1_) 4 MPI processes
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object: (PPE_mg_levels_1_sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_1_sub_) 1 MPI processes
type: icc
0 levels of fill
tolerance for zero pivot 2.22045e-14
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=81, cols=81
total: nonzeros=2091, allocated nonzeros=2091
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=338, cols=338
total: nonzeros=12942, allocated nonzeros=12942
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
Up solver (post-smoother) on level 1 -------------------------------
KSP Object: (PPE_mg_levels_1_) 4 MPI processes
type: richardson
Richardson: damping factor=0.9
maximum iterations=1
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_1_) 4 MPI processes
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object: (PPE_mg_levels_1_sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_1_sub_) 1 MPI processes
type: icc
0 levels of fill
tolerance for zero pivot 2.22045e-14
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=81, cols=81
total: nonzeros=2091, allocated nonzeros=2091
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=338, cols=338
total: nonzeros=12942, allocated nonzeros=12942
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
Down solver (pre-smoother) on level 2 -------------------------------
KSP Object: (PPE_mg_levels_2_) 4 MPI processes
type: richardson
Richardson: damping factor=0.9
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: (PPE_mg_levels_2_) 4 MPI processes
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object: (PPE_mg_levels_2_sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_2_sub_) 1 MPI processes
type: icc
0 levels of fill
tolerance for zero pivot 2.22045e-14
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=2265, cols=2265
total: nonzeros=60131, allocated nonzeros=60131
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=9124, cols=9124
total: nonzeros=267508, allocated nonzeros=267508
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
Up solver (post-smoother) on level 2 -------------------------------
KSP Object: (PPE_mg_levels_2_) 4 MPI processes
type: richardson
Richardson: damping factor=0.9
maximum iterations=1
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_2_) 4 MPI processes
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object: (PPE_mg_levels_2_sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_2_sub_) 1 MPI processes
type: icc
0 levels of fill
tolerance for zero pivot 2.22045e-14
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=2265, cols=2265
total: nonzeros=60131, allocated nonzeros=60131
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=9124, cols=9124
total: nonzeros=267508, allocated nonzeros=267508
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
Down solver (pre-smoother) on level 3 -------------------------------
KSP Object: (PPE_mg_levels_3_) 4 MPI processes
type: richardson
Richardson: damping factor=0.9
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: (PPE_mg_levels_3_) 4 MPI processes
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object: (PPE_mg_levels_3_sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_3_sub_) 1 MPI processes
type: icc
0 levels of fill
tolerance for zero pivot 2.22045e-14
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=59045, cols=59045
total: nonzeros=1504413, allocated nonzeros=1594215
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=236600, cols=236600
total: nonzeros=6183334, allocated nonzeros=12776400
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
Up solver (post-smoother) on level 3 -------------------------------
KSP Object: (PPE_mg_levels_3_) 4 MPI processes
type: richardson
Richardson: damping factor=0.9
maximum iterations=1
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using nonzero initial guess
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_3_) 4 MPI processes
type: bjacobi
block Jacobi: number of blocks = 4
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object: (PPE_mg_levels_3_sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (PPE_mg_levels_3_sub_) 1 MPI processes
type: icc
0 levels of fill
tolerance for zero pivot 2.22045e-14
using Manteuffel shift
matrix ordering: natural
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=59045, cols=59045
total: nonzeros=1504413, allocated nonzeros=1594215
total number of mallocs used during MatSetValues calls =0
not using I-node routines
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=236600, cols=236600
total: nonzeros=6183334, allocated nonzeros=12776400
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
linear system matrix = precond matrix:
Matrix Object: 4 MPI processes
type: mpiaij
rows=236600, cols=236600
total: nonzeros=6183334, allocated nonzeros=12776400
total number of mallocs used during MatSetValues calls =0
not using I-node (on process 0) routines
solver: ||b|| = 5.9221e-03
solver: ||x(0)|| = 0.0000e+00
solver: Iteration: 1 ||r|| = 2.2256e-03 ||x(i+1)-x(i)|| = 4.7864e+00 ||x(i+1)|| = 4.7864e+00
solver: Iteration: 2 ||r|| = 1.4156e-03 ||x(i+1)-x(i)|| = 5.6720e+00 ||x(i+1)|| = 1.0227e+01
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