Explicit Splitting Scheme for Maxwell’s Equations

Abstract

A new explicit scheme for the numerical integration of Maxwell’s equations in isotropic and anisotropic dielectrics and conductors is presented. In this scheme, the electric and magnetic fields are calculated at the same instants and at the same nodes of the spatial grid with splitting by spatial directions and physical processes. The scheme is conservative, monotonic, second-order accurate in time, and third-order accurate in spatial variables. In the course of simulating the propagation of low-frequency signals in the Earth-ionosphere waveguide, the scheme allows using a significantly bigger time integration step than the widely used finite-difference time domain method for the same accuracy.