The computation of linear dispersive electromagnetic waves

Numerical solutions of the equations describing electromagnetic pulse propagation in geometrically complex Debye-dispersive dielectrics are used in the development of safety standards for human exposure to non-ionizing radiation. Debye dispersion is a relaxation process, a phenomenon which occurs when the underlying material is forced into non-equilibrium due to the passing waves. This relaxation is typically stiff in applications, and the system of equations is then singularly perturbed. Such systems are notoriously expensive to solve with standard numerical methods. We review previous work related to the numerical solution of such problems, and consider a representative numerical scheme in order to elucidate the nature of the challenge posed to Computational Electromagnetics by the stiffness. Further, an analysis of the stiffness leads us to propose a scheme that seems "natural" for the problem at hand.