The paper presents a two-domain, two-step approach for simulating electromagnetic fields in a domain where eddy current effects are present only in a subset of the conductive region. The method uses the electric scalar potential and the magnetic vector potential as primary variables, and decouples them using the DC-conduction gauge and electric circuit element (ECE) boundary conditions.
In the first step (DC-conduction), the electric scalar potential is computed by solving the DC-conduction equation over the entire domain. In the second step (EC-correction), the magnetic vector potential is computed by solving the eddy current equation in the eddy current subdomain and the magneto-static equation in the magneto-static subdomain, using the electric scalar potential obtained in the first step.
The authors provide a weak formulation of the problem and discuss the discretization using finite elements. They also address the reconstruction of the voltage drop, which is important for engineering applications.
The numerical results validate the proposed approach. The authors consider three test cases: a homogeneous conductive cylinder, a three-portion cylinder with eddy currents present everywhere, and a three-portion cylinder with eddy currents present only in the ferromagnetic parts. The results show that the method accurately captures the eddy current effects and provides a computationally efficient solution compared to a full eddy current formulation.
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