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I had heard in a lecture, perhaps 15 years ago, that the vast majority of the world's HPC resources were dedicated to solving linear systems by iterative methods. I seem to remember it was 90%. I can't find a reference for a figure like this. Are there any recent estimates for this?

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  • $\begingroup$ Welcome to scicomp! Just to clearify: do you mean scientific clusters at universities, or in a more general sense of high performance computing? $\endgroup$
    – MPIchael
    Jan 11 at 16:04
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    $\begingroup$ I'm not sure if this entirely answers your question, but here is a technical report from NASA (from 2014) that discusses current usage of HPC systems for CFD work and it breaks some of this down into flops used on LINPACK routines ntrs.nasa.gov/api/citations/20140003093/downloads/… $\endgroup$
    – whpowell96
    Jan 11 at 16:14
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    $\begingroup$ Rather than "inverting matrices by iterative methods", you might say "Solving linear systems of equations by iterative methods" Actually computing inverses is seldom done in practice. Solving linear systems is most of the work in the numerical solution of partial differential equations. $\endgroup$ Jan 12 at 0:27

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The number is almost certainly unverifiable because every HPC system's overall user community is different and because there are so many systems around. I think that the number is vastly smaller than 90%: At most universities, well over half (and in some cases 80%) of cycles are used up by people doing molecular dynamics or quantum mechanics simulations of materials. MD simulations do not do much in terms of linear systems to begin with, and the quantum chemistry codes do not either.

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