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Non linear conductivity in AC

Hello,
I need to simulate the behavior of a dielectric material in AC to obtain the electric field distribution.
Normally I would use the Electrostatics study, but this material has a nonlinear dependence of the conductivity with the electric field, and the Electrostatics physic doesn't takes in account the influence of conductivity.
I tried to use the Electric currents study with a sinusoidal voltage source and a time dependent solver. The problem is, it takes a lot of time even for a 2D model.
Do you have any ideas on how to improve it? ( or even if my assumptions are wrong, I'm not absolutely sure if EC+time solver is the best model for my problem)

Thank You

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