Support for complex numbers

[benvial]

Thanks for working on this, that's a great addition to the fenics ecosystem to have autodiff with dolfinx.

I was wondering if dxa supports or plans to support complex valued PDEs (but real valued control functions) as there is optional complex number support in dolfinx?
That would be very useful for e.g wave problems.

[jorgensd]

It is a bit complicated with complex valued PDEs.
I did play around with this a while back, and the adjointing of the forward problem is ok, while the challenge is in the differentiation of the functional (Should be real valued to make sense) and with respect to the control.

At the moment DOLFINx doesn't support mixing datatypes (functions with real and complex values) in the same for, which makes it tricky to make nice for now without a lot of hacking.

This might improve in the future, ref: FEniCS/dolfinx#3880

[benvial]

Thanks for the quick answer and for pointing to this dolfinx relevant issue, will keep an eye on it.