[petsc-users] Number of levels of multigrid : 2-3 is sufficient ??

[Barry Smith]

1) Your timings are meaningless! You cannot compare timings when built with all debugging on, PERIOD! 

  ##########################################################
      #                                                        #
      #                          WARNING!!!                    #
      #                                                        #
      #   This code was compiled with a debugging option,      #
      #   To get timing results run ./configure                #
      #   using --with-debugging=no, the performance will      #
      #   be generally two or three times faster.              #
      #                                                        #
      ##########################################################

2) Please run with -snes_view . 

3) Note that with 7 levels

SNESJacobianEval      21 1.0 2.4364e+01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 54  0  0  0  0  54  0  0  0  0     0

with 2 levels

SNESJacobianEval       6 1.0 2.2441e+01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 34  0  0  0  0  34  0  0  0  0     0


The Jacobian evaluation is dominating the time! Likely if you fix the debugging this will be less the case

  Barry

> On Oct 13, 2015, at 9:23 PM, Timothée Nicolas <timothee.nicolas at gmail.com> wrote:
> 
> Dear all,
> 
> I have been playing around with multigrid recently, namely with /ksp/ksp/examples/tutorials/ex42.c, with /snes/examples/tutorial/ex5.c and with my own implementation of a laplacian type problem. In all cases, I have noted no improvement whatsoever in the performance, whether in CPU time or KSP iteration, by varying the number of levels of the multigrid solver. As an example, I have attached the log_summary for ex5.c with nlevels = 2 to 7, launched by 
> 
> mpiexec -n 1 ./ex5 -da_grid_x 21 -da_grid_y 21 -ksp_rtol 1.0e-9 -da_refine 6 -pc_type mg -pc_mg_levels # -snes_monitor -ksp_monitor -log_summary
> 
> where -pc_mg_levels is set to a number between 2 and 7.
> 
> So there is a noticeable CPU time improvement from 2 levels to 3 levels (30%), and then no improvement whatsoever. I am surprised because with 6 levels of refinement of the DMDA the fine grid has more than 1200 points so with 3 levels the coarse grid still has more than 300 points which is still pretty large (I assume the ratio between grids is 2). I am wondering how the coarse solver efficiently solves the problem on the coarse grid with such a large number of points ? Given the principle of multigrid which is to erase the smooth part of the error with relaxation methods, which are usually efficient only for high frequency, I would expect optimal performance when the coarse grid is basically just a few points in each direction. Does anyone know why the performance saturates at low number of levels ? Basically what happens internally seems to be quite different from what I would expect...
> 
> Best
> 
> Timothee
> <ex5_2_levels_of_multigrid.log><ex5_3_levels_of_multigrid.log><ex5_4_levels_of_multigrid.log><ex5_5_levels_of_multigrid.log><ex5_6_levels_of_multigrid.log><ex5_7_levels_of_multigrid.log>