Thread

1. sheafification · 1789583071 · focus · HN ↗

   I doubt outside of a few exceptional cases that one is going to do better on CPU-bound problems than a well-written LAPACK implementation built for the architecture you intend to run on.

   Maybe pedagogy was the point? I didn’t really get that from the article, maybe some intention was lost by filtering it through AI.

   1. BigTTYGothGF · 1789587563 · focus · HN ↗

      LAPACK doesn't do sparse systems.

      (On the other hand, I skimmed the article and this might be a banded system, which LAPACK can handle).

      1. sheafification · 1789591019 · focus · HN ↗

         True, 2D Poisson is only approximately banded. Still, I don’t think I’d bother rolling my own sparse solver. It’s a well-trod problem.

         1. loiseaujc · 1789630872 · focus · HN ↗

            Author here. It actually is a block tridiagonal matrix with tridiagonal blocks. The test problem only has a quarter millions of unknowns so, for a production run, I wouldn't bother write my own sparse solver either. Here, it is done mainly for the sake of pedagogy to help students understand the interplay between a mathematical algorithm that looks good on paper and its hardware implementation which is not as promising as one would expect.

            Jacobi and Gauss-Seidel wouldn't be solvers I'd even consider for a real problem. But they are simple enough that anyone with a basic understanding of linear algebra and programming can follow along. But much research requires me to run simulations on thousands (if not hundreds of thousands) of cores, and there, off-the-shelf solver implementations will often not cut it.

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