Not my area of expertise, but I was under the impression that finite element analysis, like other sparse algebra problems, are reasonably well suited for GPUs, which are much more parallel than 2 or 3 cores. Have you looked into that?

The time domain codes work well with GPUs and multiple cores, but the frequency domain ones don’t. I don’t know enough of what’s going on under the hood, but it’s like that for all of them.

I've worked with applied math PDE people and they use supercomputers to full effect. Granted it's a real pain and your cross connect bandwidth matters (hence supercomputer), but you can scale up pretty well.

I thought FE was mostly memory bandwidth bound?