A New Stable Full-Wave Maxwell Solver for All Frequencies

Magnetic vector potential (MVP) formulations are widely used in the electromagnetic (EM) field computation. For problems with both inductive and capacitive effects, existing full-wave MVP formulations are mostly nonuniquely solvable, and sophisticated preconditioners are indispensable when solving these resultant linear matrix equations. To find a stable formulation with a unique solution, it is important to incorporate the necessary physics equations and the gauge condition properly. Traditional Coulomb-gauged formulation using the penalty technique does not work for edge elements, since the divergence of the edge element basis function is zero within each element. In this paper, a novel MVP formulation with Coulomb gauge for full-wave Maxwell equations using edge elements is proposed in the frequency domain. Extensive numerical examples are computed to show that the proposed formulation is stable even for tiny frequencies, which is very useful in full-wave engineering EM field computation.