Plane Wave Discontinuous Galerkin Method with Lagrange Multipliers for Solving Time-Harmonic Maxwell's Equations in Three Dimensions

A discontinuous Galerkin method is formulated with plane wave basis functions and Lagrange multipliers, and it is investigated for solving vector curl-curl equations derived from Maxwell's equations. This method was previously developed for solving the scalar Helmholtz equation in both two and three dimensions. By defining vector plane waves and vector Lagrange multipliers within tetrahedral elements and on element boundaries, this algorithm is extended to solve three-dimensional vector problems for electromagnetic analysis. Numerical results for wave propagation in free space and scattering by a perfectly electrically conducting sphere are presented to validate the proposed method and evaluate its potential capability.