Magnetic Scalar Potential Formulations for the Fast Solution of 3D Eddy-Current Problems in Multiply-Connected Domains
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The solution of time-harmonic eddy current problems becomes challenging when large-scale engineering applications have to be simulated. In fact, FEM-based commercial software most often implements a magnetic vector potential edge-element (A,v-A) formulation, leading to a large number of degrees of freedom (DOFs). These can be reduced by introducing a magnetic scalar potential in the air region, which however becomes difficult with multiply-connected domains. A numerical procedure for calculating in linear-time the cohomology group needed for introducing the scalar potential in multiply connected regions is presented. Based on this algorithm, magnetic scalar potential formulations are proposed. These formulations are able to provide very accurate numerical results, with a minimum amount of DOFs to represent the eddy current model.
