Distributed array to solve a system of linear equations on a cluster

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I'm trying to solve a system of linear equations in parallel on a computing cluster using iterative methods and distributed arrays. Right now my code looks like:
cores = 42;
cluster = parcluster;
K_solve_dist = distributed(K_solve);
force_vec_solv_dist = distributed(force_vec_solv);
[res_disp, flag_solv{ii,kk}(n,1)] = cgs(K_solve_dist,force_vec_solv_dist,tol_iter,max_iter);
However, regardless of how many cores I use, the run time seems to stay they same (this runtime is also the same as if I don't use distributed arrays at all). If I run it without the line "parpool(cluster,cores)" it runs almost 50% faster, but only uses 12 cores, even though there are more cores available. I'm trying to figure out if there's a way to use more than 12 cores and speed up the time it takes to preform this calculation.

Answers (1)

Sam Marshalik
Sam Marshalik on 7 Dec 2021
Hey Melissa,
I would not think of distributed arrays as a way to speed up your computation. Distributed arrays are useful for when something does not fit into your machine's memory, so you spread the content of the matrix across multiple machines. This will not cause the code to run faster and in fact, like you saw, will probably run it slower, since you are introducing the overhead of communication into the equation.
It is worth pointing out that using distributed arrays on a single machine will not give you any benefit, since you are still limited to that one computer's hardware. If you have access to MATLAB Parallel Server on your cluster, then using distributed arrays with your computation will be helpful.
In short, you will truly see the benefit of using distributed arrays when you are working with very large data that can't fit on one machine. If you want to try to speed things up, you will want to take a look at things such as parfor, parfeval, gpuArray, and such parallel constructs.
Joss Knight
Joss Knight on 10 Dec 2021
gpuArray supports all the iterative solvers including cgs. However, it is mainly optimized for sparse matrices. If your matrix is dense you'll be better off using a direct solver (i.e. mldivide). This is of course also supported by gpuArray.

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