Inquiry about Preconditioned Iterative Solvers for Complex-Valued Systems

[Jinqiang Chen]

Hello,

I am currently working with complex-valued linear systems derived from electromagnetic wave simulations. While studying step-29, step-58, and step-81, I noticed that the built-in GMRES solver appears to be designed exclusively for double-precision real arithmetic.

Could you kindly advise if there are alternative approaches to solve complex-valued systems natively using preconditioned iterative methods (e.g., GMRES for complex numbers) within deal.II?  

I would greatly appreciate any guidance, code snippets, or references to relevant discussions.

Best,

Jinqiang

[Wolfgang Bangerth]

Jinqiang:

This issue has come up a number of times in the past, and there is a note I
imagine you've already seen in step-58:
https://dealii.org/developer/doxygen/deal.II/step_58.html#step_58-Betterlinearsolvers
So, yes, it would be nice to have these solvers, but we don't currently other
than the ability to solve complex-valued problems with SparseDirectUMFPACK.

It is possible that PETSc's implementation of GMRES can solve complex-valued
problems and that that gives you an option. You might want to check that. It
is a bit of a hassle to use PETSc for complex-valued problems because you have
to re-compile all of PETSc and then all of deal.II for that. But it's an idea.

Of course, if you wanted to think about what one would need to do to extend
our own GMRES implementation for complex-valued problems, that would be fantastic!

Best
W.