Continuous potential Maxwell solutions on nodal-based finite elements

Abstract

A nodal-based finite-element approach for computing electric fields in heterogeneous media is presented. The primary calculation is formulated in terms of continuous potentials, so that no special care is required on element assembly at dielectric interfaces. The resulting Galerkin weak-form matrices exhibit the special Helmholtz structure, which guarantees the absence of parasitic solutions in driven problems with physically well-posed boundary conditions. The enhanced sparsity of the Helmholtz form mitigates the extra coupling effort associated with introduction of a fourth degree of freedom relative to direct E solution. E can be extracted from the computed potentials as a postprocessing step either at nodal positions or element centroids. Solutions obtained with this approach for several benchmark and practical problems are shown to be parasite-free and essentially indistinguishable from previously reported direct E computations.