[petsc-users] GAMG for the unsymmetrical matrix
Kong, Fande
fande.kong at inl.gov
Wed Apr 12 18:04:12 CDT 2017
On Sun, Apr 9, 2017 at 6:04 AM, Mark Adams <mfadams at lbl.gov> wrote:
> You seem to have two levels here and 3M eqs on the fine grid and 37 on
> the coarse grid. I don't understand that.
>
> You are also calling the AMG setup a lot, but not spending much time
> in it. Try running with -info and grep on "GAMG".
>
I got the following output:
[0] PCSetUp_GAMG(): level 0) N=3020875, n data rows=1, n data cols=1,
nnz/row (ave)=71, np=384
[0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
73.6364 nnz ave. (N=3020875)
[0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
[0] PCGAMGProlongator_AGG(): New grid 18162 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.978702e+00
min=2.559747e-02 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Aggregate processors noop: new_size=384,
neq(loc)=40
[0] PCSetUp_GAMG(): 1) N=18162, n data cols=1, nnz/row (ave)=94, 384 active
pes
[0] PCSetUp_GAMG(): 2 levels, grid complexity = 1.00795
[0] PCSetUp_GAMG(): level 0) N=3020875, n data rows=1, n data cols=1,
nnz/row (ave)=71, np=384
[0] PCGAMGFilterGraph(): 100.% nnz after filtering, with threshold 0.,
73.6364 nnz ave. (N=3020875)
[0] PCGAMGCoarsen_AGG(): Square Graph on level 1 of 1 to square
[0] PCGAMGProlongator_AGG(): New grid 18145 nodes
[0] PCGAMGOptProlongator_AGG(): Smooth P0: max eigen=1.978584e+00
min=2.557887e-02 PC=jacobi
[0] PCGAMGCreateLevel_GAMG(): Aggregate processors noop: new_size=384,
neq(loc)=37
[0] PCSetUp_GAMG(): 1) N=18145, n data cols=1, nnz/row (ave)=94, 384 active
pes
[0] PCSetUp_GAMG(): 2 levels, grid complexity = 1.00792
GAMG specific options
PCGAMGGraph_AGG 40 1.0 8.0759e+00 1.0 3.56e+07 2.3 1.6e+06 1.9e+04
7.6e+02 2 0 2 4 2 2 0 2 4 2 1170
PCGAMGCoarse_AGG 40 1.0 7.1698e+01 1.0 4.05e+09 2.3 4.0e+06 5.1e+04
1.2e+03 18 37 5 27 3 18 37 5 27 3 14632
PCGAMGProl_AGG 40 1.0 9.2650e-01 1.2 0.00e+00 0.0 9.8e+05 2.9e+03
9.6e+02 0 0 1 0 2 0 0 1 0 2 0
PCGAMGPOpt_AGG 40 1.0 2.4484e+00 1.0 4.72e+08 2.3 3.1e+06 2.3e+03
1.9e+03 1 4 4 1 4 1 4 4 1 4 51328
GAMG: createProl 40 1.0 8.3786e+01 1.0 4.56e+09 2.3 9.6e+06 2.5e+04
4.8e+03 21 42 12 32 10 21 42 12 32 10 14134
GAMG: partLevel 40 1.0 6.7755e+00 1.1 2.59e+08 2.3 2.9e+06 2.5e+03
1.5e+03 2 2 4 1 3 2 2 4 1 3 9431
>
>
> On Fri, Apr 7, 2017 at 5:29 PM, Kong, Fande <fande.kong at inl.gov> wrote:
> > Thanks, Barry.
> >
> > It works.
> >
> > GAMG is three times better than ASM in terms of the number of linear
> > iterations, but it is five times slower than ASM. Any suggestions to
> improve
> > the performance of GAMG? Log files are attached.
> >
> > Fande,
> >
> > On Thu, Apr 6, 2017 at 3:39 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >>
> >>
> >> > On Apr 6, 2017, at 9:39 AM, Kong, Fande <fande.kong at inl.gov> wrote:
> >> >
> >> > Thanks, Mark and Barry,
> >> >
> >> > It works pretty wells in terms of the number of linear iterations
> (using
> >> > "-pc_gamg_sym_graph true"), but it is horrible in the compute time. I
> am
> >> > using the two-level method via "-pc_mg_levels 2". The reason why the
> compute
> >> > time is larger than other preconditioning options is that a matrix
> free
> >> > method is used in the fine level and in my particular problem the
> function
> >> > evaluation is expensive.
> >> >
> >> > I am using "-snes_mf_operator 1" to turn on the Jacobian-free Newton,
> >> > but I do not think I want to make the preconditioning part
> matrix-free. Do
> >> > you guys know how to turn off the matrix-free method for GAMG?
> >>
> >> -pc_use_amat false
> >>
> >> >
> >> > Here is the detailed solver:
> >> >
> >> > SNES Object: 384 MPI processes
> >> > type: newtonls
> >> > maximum iterations=200, maximum function evaluations=10000
> >> > tolerances: relative=1e-08, absolute=1e-08, solution=1e-50
> >> > total number of linear solver iterations=20
> >> > total number of function evaluations=166
> >> > norm schedule ALWAYS
> >> > SNESLineSearch Object: 384 MPI processes
> >> > type: bt
> >> > interpolation: cubic
> >> > alpha=1.000000e-04
> >> > maxstep=1.000000e+08, minlambda=1.000000e-12
> >> > tolerances: relative=1.000000e-08, absolute=1.000000e-15,
> >> > lambda=1.000000e-08
> >> > maximum iterations=40
> >> > KSP Object: 384 MPI processes
> >> > type: gmres
> >> > GMRES: restart=100, using Classical (unmodified) Gram-Schmidt
> >> > Orthogonalization with no iterative refinement
> >> > GMRES: happy breakdown tolerance 1e-30
> >> > maximum iterations=100, initial guess is zero
> >> > tolerances: relative=0.001, absolute=1e-50, divergence=10000.
> >> > right preconditioning
> >> > using UNPRECONDITIONED norm type for convergence test
> >> > PC Object: 384 MPI processes
> >> > type: gamg
> >> > MG: type is MULTIPLICATIVE, levels=2 cycles=v
> >> > Cycles per PCApply=1
> >> > Using Galerkin computed coarse grid matrices
> >> > GAMG specific options
> >> > Threshold for dropping small values from graph 0.
> >> > AGG specific options
> >> > Symmetric graph true
> >> > Coarse grid solver -- level -------------------------------
> >> > KSP Object: (mg_coarse_) 384 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: (mg_coarse_) 384 MPI processes
> >> > type: bjacobi
> >> > block Jacobi: number of blocks = 384
> >> > Local solve is same for all blocks, in the following KSP and
> >> > PC objects:
> >> > 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
> >> > [INBLOCKS]
> >> > matrix ordering: nd
> >> > factor fill ratio given 5., needed 1.31367
> >> > Factored matrix follows:
> >> > Mat Object: 1 MPI processes
> >> > type: seqaij
> >> > rows=37, cols=37
> >> > package used to perform factorization: petsc
> >> > total: nonzeros=913, allocated nonzeros=913
> >> > total number of mallocs used during MatSetValues
> calls
> >> > =0
> >> > not using I-node routines
> >> > linear system matrix = precond matrix:
> >> > Mat Object: 1 MPI processes
> >> > type: seqaij
> >> > rows=37, cols=37
> >> > total: nonzeros=695, allocated nonzeros=695
> >> > total number of mallocs used during MatSetValues calls =0
> >> > not using I-node routines
> >> > linear system matrix = precond matrix:
> >> > Mat Object: 384 MPI processes
> >> > type: mpiaij
> >> > rows=18145, cols=18145
> >> > total: nonzeros=1709115, allocated nonzeros=1709115
> >> > 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_) 384 MPI processes
> >> > type: chebyshev
> >> > Chebyshev: eigenvalue estimates: min = 0.133339, max =
> >> > 1.46673
> >> > Chebyshev: eigenvalues estimated using gmres with
> translations
> >> > [0. 0.1; 0. 1.1]
> >> > KSP Object: (mg_levels_1_esteig_) 384 MPI
> >> > processes
> >> > type: gmres
> >> > GMRES: restart=30, using Classical (unmodified)
> >> > Gram-Schmidt Orthogonalization with no iterative refinement
> >> > GMRES: happy breakdown tolerance 1e-30
> >> > maximum iterations=10, initial guess is zero
> >> > tolerances: relative=1e-12, absolute=1e-50,
> >> > divergence=10000.
> >> > left preconditioning
> >> > using PRECONDITIONED norm type for convergence test
> >> > 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_) 384 MPI processes
> >> > type: sor
> >> > SOR: type = local_symmetric, iterations = 1, local
> iterations
> >> > = 1, omega = 1.
> >> > linear system matrix followed by preconditioner matrix:
> >> > Mat Object: 384 MPI processes
> >> > type: mffd
> >> > rows=3020875, cols=3020875
> >> > Matrix-free approximation:
> >> > err=1.49012e-08 (relative error in function evaluation)
> >> > Using wp compute h routine
> >> > Does not compute normU
> >> > Mat Object: () 384 MPI processes
> >> > type: mpiaij
> >> > rows=3020875, cols=3020875
> >> > total: nonzeros=215671710, allocated nonzeros=241731750
> >> > 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)
> >> > linear system matrix followed by preconditioner matrix:
> >> > Mat Object: 384 MPI processes
> >> > type: mffd
> >> > rows=3020875, cols=3020875
> >> > Matrix-free approximation:
> >> > err=1.49012e-08 (relative error in function evaluation)
> >> > Using wp compute h routine
> >> > Does not compute normU
> >> > Mat Object: () 384 MPI processes
> >> > type: mpiaij
> >> > rows=3020875, cols=3020875
> >> > total: nonzeros=215671710, allocated nonzeros=241731750
> >> > total number of mallocs used during MatSetValues calls =0
> >> > not using I-node (on process 0) routines
> >> >
> >> >
> >> > Fande,
> >> >
> >> > On Thu, Apr 6, 2017 at 8:27 AM, Mark Adams <mfadams at lbl.gov> wrote:
> >> > On Tue, Apr 4, 2017 at 10:10 AM, Barry Smith <bsmith at mcs.anl.gov>
> wrote:
> >> > >
> >> > >> Does this mean that GAMG works for the symmetrical matrix only?
> >> > >
> >> > > No, it means that for non symmetric nonzero structure you need the
> >> > > extra flag. So use the extra flag. The reason we don't always use
> the flag
> >> > > is because it adds extra cost and isn't needed if the matrix
> already has a
> >> > > symmetric nonzero structure.
> >> >
> >> > BTW, if you have symmetric non-zero structure you can just set
> >> > -pc_gamg_threshold -1.0', note the "or" in the message.
> >> >
> >> > If you want to mess with the threshold then you need to use the
> >> > symmetrized flag.
> >> >
> >>
> >
>
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