Does anybody have good references in the literature analyzing the memory access patterns for sparse solvers and how they scale? I remember seeing Barry's talk about multigrid memory access patterns, but I'm not sure if I've ever seen a good paper reference.
Cheers, Aron On Wed, Nov 18, 2009 at 6:14 PM, Satish Balay <balay at mcs.anl.gov> wrote: > Just want to add one more point to this. > > Most multicore machines do not provide scalable hardware. [yeah - the > FPUs cores are scalable - but the memory subsystem is not]. So one > should not expect scalable performance out of them. You should take > the 'max' performance you can get out out them - and then look for > scalability with multiple nodes. > > Satish > > On Wed, 18 Nov 2009, Jed Brown wrote: > > > jarunan at ascomp.ch wrote: > > > > > > Hello, > > > > > > I have read the topic about performance of a machine with 2 dual-core > > > chips, and it is written that with -np 2 it should scale the best. I > > > would like to ask about 4-core machine. > > > > > > I run the test on a quad core machine with mpiexec -n 1, 2 and 4 to see > > > the parallel scaling. The cpu times of the test are: > > > > > > Solver/Precond/Sub_Precond > > > > > > gmres/bjacobi/ilu > > > > > > -n 1, 1917.5730 sec, > > > -n 2, 1699.9490 sec, efficiency = 56.40% > > > -n 4, 1661.6810 sec, efficiency = 28.86% > > > > > > bicgstab/asm/ilu > > > > > > -n 1, 1800.8380 sec, > > > -n 2, 1415.0170 sec, efficiency = 63.63% > > > -n 4, 1119.3480 sec, efficiency = 40.22% > > > > These numbers are worthless without at least knowing iteration counts. > > > > > Why is the scaling so low, especially with option -n 4? > > > Would it be expected to be better running with real 4 CPU's instead of > a > > > quad core ship? > > > > 4 sockets using a single core each (4x1) will generally do better than > > 2x2 or 1x4, but 4x4 costs about the same as 4x1 these days. This is a > > very common question, the answer is that a single floating point unit is > > about 10 times faster than memory for the sort of operations that we do > > when solving PDE. You don't get another memory bus every time you add a > > core so the ratio becomes worse. More cores are not a complete loss > > because at least you get an extra L1 cache for each core, but sparse > > matrix and vector kernels are atrocious at reusing cache (there's not > > much to reuse because most values are only needed to perform one > > operation). > > > > Getting better multicore performance requires changing the algorithms to > > better reuse L1 cache. This means moving away from assembled matrices > > where possible and of course finding good preconditioners. High-order > > and fast multipole methods are good for this. But it's very much an > > open problem and unless you want to do research in the field, you have > > to live with poor multicore performance. > > > > When buying hardware, remember that you are buying memory bandwidth (and > > a low-latency network) instead of floating point units. > > > > Jed > > > > > > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20091118/1fdcbea5/attachment.htm>
