New Feature: GPU Mode Solving

[hammy4815]

There was an effort to vectorize electromagnetic python (EMpy) mode solving on a gpu (hence the name EMpy_gpu) for my cloned dependency of EMEPy. I didn't get it to work at the time and gave up early but it should be able to be done. We may want to use a modified version of EMpy again but different.

[hammy4815]

Note: we are keeping the empy mode solver only because it supports a full permittivity tensor. Otherwise, we are migrating towards tidy3d. I recommend trying to gpu-ize tidy3d instead since it is easier to use, has PML, has bends, and is faster

[smartalecH]

The hardest thing about throwing a mode solver on the gpu right now is finding a suitable targeted eigensolver compatible with complex, sparse matrices. Unfortunately, none of the "popular" wrapper packages (torch, jax, pycuda, etc) seem to support this.

Furthermore, we probably want to offload the entire kernel to the gpu, not just the mode solving section.

[hammy4815]

@smartalecH ,

Do you mean the entire EME process onto the gpu?

[smartalecH]

Yes. Mode calculation + mode overlap + Redheffer Star product.

[hammy4815]

@smartalecH ,

Mode calculation + mode overlap - easy. We can reformulate the Mode object in a simple way on the gpu

Redheffer star product, not possible with Simphony (without forking and reformulating it). We could use sax however if we wanted it there. Doing so would require modifying about half the code in the repo however

[smartalecH]

I would just write a quick function that does it. It's rather easy and has been done in dozens of packages already.

[hammy4815]

@smartalecH ,

It's easy for small-port systems. But when you have different numbers of ports on each side of an interface, with lots of modes, can't it get tricky?