On Wed, Oct 14, 2015 at 7:34 AM, Timothée Nicolas < [email protected]> wrote:
> OK, I see. Does it mean that the coarse grid solver is by default set up > with the options -ksp_type preonly -pc_type lu ? What about the > multiprocessor case ? > Small scale: We use redundant LU Large Scale: We use GAMG Matt > Thx > > Timothee > > 2015-10-14 21:22 GMT+09:00 Matthew Knepley <[email protected]>: > >> On Tue, Oct 13, 2015 at 9:23 PM, Timothée Nicolas < >> [email protected]> 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... >>> >> >> A performance model that counts only flops is not sophisticated enough to >> understand this effect. Unfortunately, nearly all MG >> books/papers use this model. What we need is a model that incorporates >> memory bandwidth (for pulling down the values), and >> also maybe memory latency. For instance, your relaxation pulls down all >> the values and makes a little progress. It does few flops, >> but lots of memory access. An LU solve does a little memory access, many >> more flops, but makes a lots more progress. If memory >> access is more expensive, then we have a tradeoff, and can understand >> using a coarse grid which is not just a few points. >> >> Thanks, >> >> Matt >> >> >>> Best >>> >>> Timothee >>> >> >> >> >> -- >> What most experimenters take for granted before they begin their >> experiments is infinitely more interesting than any results to which their >> experiments lead. >> -- Norbert Wiener >> > > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener
