Fast solution of time domain Maxwell's equations using large time steps

Abstract

A Large Time Step (LTS) method is used in the Finite Volume Time Domain (FVTD) framework for the solution of time domain Maxwell's equations. The LTS method [1] was originally proposed for the numerical solution of nonlinear hyperbolic conservation laws, as a generalization of the classical Godunov's approach which requires Riemann problems to be solved at individual cell faces in a finite volume framework. The LTS method allows the use of time steps much larger than that dictated by the Courant-Friedrich-Lewy (CFL) stability criterion for numerical solution of wave dominated problems. Long simulation times are a major concern in electromagnetic scattering problems involving large electrical sizes and re-entrant structures. The use of very large time steps in the propagation of EM waves both in freespace and multiple media is demonstrated in this work using a LTS based FVTD method.