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I have a sparse $2\times10^5$ by $2\times10^5$ matrix with $3.2\times10^9$ non-zero elements.

I want a sparse solver with out-of-core functionality. I have attempted to use Intel's MKL pardiso, with a varying degree of success. For smaller problems, it is stellar, but for the problem size above, it is taking a huge amount of RAM (even with the out-of-core enabled), presumably during fill-in reducing ordering stage.

The intel staff has been incredibly helpful with debugging several problems, but I feel that it might be prudent to try a different solver.

Is there any good reference comparing the performance of solvers for big problems?

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  • $\begingroup$ Does your problem has a structure that could be exploited ? You used a sparse direct solver, would it be possible to use an iterative solver instead ? (conjugate gradient), that has smaller memory requirements. $\endgroup$ – BrunoLevy Oct 21 '15 at 10:06
  • $\begingroup$ The matrices in question have very little structure. They are not symmetric, nor diagonal. However, the non-zeros for each row are contiguous (i.e. there are no zeros interrupting a stretch of values). That's the strongest claim I can make about the structure. $\endgroup$ – ivan-k Oct 21 '15 at 17:59
  • $\begingroup$ and did you try an iterative solver ? (GMRES or BiCGSTAB for instance), with compressed row storage, it may fit in RAM. Do you have an idea of the conditioning ? $\endgroup$ – BrunoLevy Oct 21 '15 at 21:05
  • $\begingroup$ I did not try any iterative solvers - I suppose that is a reasonable next step. I would need to run some calculations to figure out the condition numbers for the problem. My guess is that they will vary wildly with the parameters. $\endgroup$ – ivan-k Oct 22 '15 at 4:23
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If you decide to go with a direct solver, you may consider the following options:

  • Intel MKL Pardiso, which you have already tried
  • MUMPS, that is another very popular choice for parallel direct solvers and has an out-of-core capability
  • HSL, free for academic use, consider HSL_MA78, sparse out-of-core solver

Several years ago, I added to my collection the following paper that compares the performance of those three libraries for Navier-Stokes FEM:

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