Robust full‐wave Maxwell solver in time‐domain using magnetic vector potential with edge elements

Abstract

Magnetic vector potential (MVP) formulations are widely used in low-frequency eddy-current computation. For full-wave Maxwell problems with coupled resistive, inductive and capacitive effects, existing MVP formulations are either ungauged or with too complicated stabilisation procedure or with non-symmetric system matrix. Since sophisticated preconditioners are necessary to ensure good convergence rates of iterative solvers when used to solve the resultant linear system, it is also important to investigate symmetric gauged formulations which can be solved by more robust state-of-the-art sparse direct solvers. Traditional Coulomb gauged formulation using penalty technique is not feasible for edge elements since the divergence of the edge element basis function is zero within each element. In this study, a novel MVP formulation with Coulomb Gauge for full-wave Maxwell problems using edge elements is proposed. The proposed formulation is symmetric and stable for all frequencies, easy to implement and uniquely solvable. Numerical results obtained using the proposed MVP formulation are demonstrated to showcase its stability and accuracy. The method is very promising in further engineering applications.