Hi, folks. Is there a well established way to solve a linear system (normal, fully populated, Ax=b) across several nodes with Julia? Using MPI or something. I looked around and couldn’t find anything. Thanks!

[image] Ribeiro: Is there a well established way to solve a linear system (normal, fully populated, Ax=b) across several nodes with Julia? Using MPI or something. There is MUMPS.jl if you want to use a sparse-direct solve, and Elemental.jl for dense direct solves. For distributed-memory spar…

Thanks for the info. The matrix A is not sparse (neither is it symmetric, all positive, etc.). Think A=rand(1000,1000); b=rand(1000);. My main problem is not distributing A in memory (it fits in my RAM), but the actual computation of x, which can take ~10 seconds and is something I must do ~1000 t…

10s per solve for 1000 solves is only like 3 hours of runtime. So you reach that goal faster by using the simple code you have now than by trying to come up with something faster :wink: Apart from that, I don’t think you can orders of magnitude in speed by using better libraries. If your solves are…

[image] Ribeiro: The matrix A is not sparse (neither is it symmetric, all positive, etc.). Think A=rand(1000,1000); b=rand(1000);. My main problem is not distributing A in memory (it fits in my RAM), but the actual computation of x, which can take ~10 seconds and is something I must do ~1000 ti…

@stevengj The matrix is between 1000x1000 and 50000x50000. I do use a multithreaded solver (IterativeSolvers.gmres!). It’s a time-marching scheme, so the linear systems are sequential. The matrix changes every time. Sometimes, it changes very little. The right hand side also changes. Also sometim…

[image] Ribeiro: I do use a multithreaded solver (IterativeSolvers.gmres!). In general, I wouldn’t use gmres for dense matrices. It will usually be faster to use a direct factorization. (Also, IterativeSolvers.gmres! is only multi-threaded insofar as the matrix×vector operations are multi-t…

@stevengj When the problem is small, I use x=A\b, which works great. For bigger problems, that does not work. I believe this is doing LU factorization (doing a manual LU takes about the same time). Doing LU for large matrices becomes quite expensive and also forces me to store another huge matrix in…

You might consider doing the LU in lower precision and using iterative refinement. The unregistered package at MultiPreicsionArrays.jl might help you. However, it’s in a very, very early stage of development and does not explicitly support distributed memory. Using the lower precision LU as a prec…

[image] Ribeiro: It seems IterativeSolvers.gmres! has options for a left and a right preconditioner. I think the standard would be to use L+I as the left preconditioner and not use a right preconditioner at all, right? Is this what you’re suggesting? No. Suppose that you have matrices A = A_…

Sorry, I’m struggling to do what you guys are proposing. using IterativeSolvers using LinearAlgebra N = 100; A = rand(N,N); b = rand(N); x = A\b; L,U=lu(A); x1 = ones(N); gmres!(x1,A,b;Pl=(L*U)\(A*x1)); The last line fails (ERROR: MethodError: no method matching ldiv!(::Vector{Float64}, ::SubArr…

MPI/Distributed linear system solver?

New to Julia

PeterSimon October 26, 2023, 8:42pm 20

Here is a link to a post providing a justification and pseudo-code for the complete implementation of the iterative refinement technique, essentially the same as @ctkelley suggested.

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MPI/Distributed linear system solver?

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