Hypre AMS Preconditioner for Complex System

Dear FEniCS Users,

My problem is somehow related to the previous question: Preconditioner for indefinite linear system

I would like to solve some Eddy Current problems using the Curl-Curl Formulation with edge elements. Starting from the undocumented curl-curl demo CG solver combinded with the Hypre AMS preconditioner works very well for time-domain problems.

For frequency domain problems I splitted the complex equations into real and imaginary part (since I am not using complex-number support yet). Setup a MixedFunctionSpace and solving with MUMPS also seems to work. But how can I get the AMS Preconditioner working?

I tried to setup a PETSc field-split preconditioner, using defining the AMS preconditioner for each diagonal block, but the performance is very bad.

Is there a “default” procedure to get a working preconditioner for a complex problem, if one has a proper method for the real-valued case?
Would the new complex number support solve my problem? Could i the simply use the complex Hypre AMS method for one complex Functionspace?

thanks for any advice
best wishes
Florian

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