A Leapfrogging Time-Domain Integral Equation Solver for Dielectric Bodies

Time-domain integral equation (TDIE) solvers for analyzing electromagnetic scattering from homogenous dielectric bodies exhibit distinct advantages over their differential equation counterparts. In this paper, a novel time-domain integral equation (TDIE) scheme that solves for either electric or magnetic current coefficients at each half time step is described. Two uniform temporal grids that are staggered by half a time step are used. This results in a non-causal system of equations for the unknown current coefficients, which is cast into a causal form by means of a band-limited extrapolation procedure and then solved by leapfrogging in time. Compared to standard solution approaches, the leapfrogging scheme is more efficient as it solves a smaller set of equations at each time step while being highly amenable to hybridization with differential equation based solvers. Furthermore, the leapfrogging scheme does not lead to loss of accuracy/stability and does not prevent acceleration by fast algorithms