Continuous potential Maxwell solutions on nodal-based finite elements

The primary calculation of the present nodal-based FEM approach for computing electric fields in heterogeneous media is formulated in terms of continuous potentials; no special care is therefore required during element assembly at dielectric surfaces. The Galerkin weak form matrices thus obtained exhibit the Helmholtz structure that guarantees the absence of parasitic solutions, where the driven problems have physically well-posed boundary conditions. Solutions obtained with this approach for both benchmark and practical problems are found to be parasite-free and virtually indistinguishable from previous direct E computations.