Hello,
one big difference is that in 3D you have "many" negative eigenvalues, evaluating the biform with any gradient field leads to the negative sign.
A simple method is the "shifted Laplacian" preconditioning: Setup a second, artificial biform with volume damping, build the preconditioner for the artificial problem, and use it to solve the original equation:
Code:
apre = ngsolve.BilinearForm(fes)
apre += p * (ngsolve.curl(u) * ngsolve.curl(w)) * ngsolve.dx
apre += -(1+1j)*(k0 ** 2) * q * (u * w) * ngsolve.dx
pre = ngsolve.Preconditioner(apre, "bddc")
Be careful to choose the sign of the imaginary part of the L2-coefficient according to damping, when you have also physical damping.
It still takes many iterations, and you may have to play with the damping coefficient.
Some references are: Erlangga, Vuik and Oosterlee
www.sciencedirect.com/science/article/abs/pii/S0168927404000091
or
link.springer.com/content/pdf/10.1007/s11831-007-9013-7.pdf
Best, Joachim