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 ?
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 >
