A Symmetric Field-Circuit Coupled Formulation for 3-D Transient Full-Wave Maxwell Problems

In this paper, a symmetric field-circuit coupled finite element method for low-frequency full-wave Maxwell problems using a magnetic vector potential formulation is proposed. The resultant fully discrete coefficient matrix is made symmetric for the first time by introducing the so-called source electric scalar potential for solid conductors, where the terminal currents are converted from the surface integrations of the current density vectors to volumetric integrations. The numerical examples, including a benchmark capacitor charging problem with external circuit connections, are solved, and the numerical results match well with the reference solutions. The proposed formulation is useful when analyzing electromagnetic fields with coupled inductive-capacitive effects and external circuit connections.