Re: [petsc-users] GAMG speed

[Michele Rosso]

Barry,
you are correct, I did not use it. I think I get now where is the 
problem. Correct me if I am wrong, but for the
geometric multigrid to work, ksp must be provided with subroutines to 
compute the matrix and the rhs at any level through
KSPSetComputeOperators and KSPSetComputeRHS.
I do not do that, I simply build a rhs vector and a matrix and then I 
solve the system.
If you confirm what I just wrote, I will try to modify my code 
accordingly and get back to you.
Thank you,
Michele
On 08/01/2013 11:48 AM, Barry Smith wrote:
   Do you use KSPSetDM(ksp,da);  ?  See src/ksp/ksp/examples/tutorials/ex19.c

    Barry

On Aug 1, 2013, at 1:35 PM, Michele Rosso <mro...@uci.edu> wrote:

Barry,

I am using a finite difference Cartesian uniform grid and DMDA and so far it 
has not given me any problem.
I am using a ksp solver (not snes). In a previous thread, I was told an odd 
number of grid points was needed for the geometric multigrid, is that correct?
I tried to run my case with


-pc_type mg -da_refine 4



but it does not seem to use the -da_refine option:

mpiexec   -np 4 ./test  -pc_type mg -da_refine 4  -ksp_view -options_left


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: mg
    MG: type is MULTIPLICATIVE, levels=1 cycles=v
      Cycles per PCApply=1
      Not using Galerkin computed coarse grid matrices
  Coarse grid solver -- level -------------------------------
    KSP Object:    (mg_levels_0_)     4 MPI processes
      type: chebyshev
        Chebyshev: eigenvalue estimates:  min = 0.134543, max = 1.47998
        Chebyshev: estimated using:  [0 0.1; 0 1.1]
        KSP Object:        (mg_levels_0_est_)         4 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-05, absolute=1e-50, divergence=10000
          left preconditioning
          using NONE norm type for convergence test
        PC Object:        (mg_levels_0_)         4 MPI processes
          type: sor
            SOR: type = local_symmetric, iterations = 1, local iterations = 1, 
omega = 1
          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
      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_levels_0_)     4 MPI processes
      type: sor
        SOR: type = local_symmetric, iterations = 1, local iterations = 1, 
omega = 1
      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
  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
Solution       =    1.53600013     sec
#PETSc Option Table entries:
-da_refine 4
-ksp_view
-options_left
-pc_type mg
#End of PETSc Option Table entries
There is one unused database option. It is:
Option left: name:-da_refine value: 4

Michele

On 08/01/2013 11:21 AM, Barry Smith wrote:
    What kind of mesh are you using? Are you using DMDA? If you are using DMDA (and have 
written your code to use it "correctly") then it should be trivial to run with 
geometric multigrid and geometric multigrid should be a bit faster.

    For example on src/snes/examples/tutorials/ex19.c   I run with ./ex19 
-pc_type mg -da_refine 4 and it refines the original DMDA 4 times and uses 
geometric multigrid with 5 levels.


    Barry


On Aug 1, 2013, at 1:14 PM, Michele Rosso <mro...@uci.edu> wrote:

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