High-order accurate modeling of electromagnetic wave propagation across media – Grid conforming bodies Eugene Kashdan 1 , Eli Turkel * School of Mathematical Sciences, Department of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel Received 11 December 2005; received in revised form 9 March 2006; accepted 9 March 2006 Abstract The Maxwell equations contain a dielectric permittivity e that describes the particular media. For homogeneous mate- rials at low temperatures this coefficient is constant within a material. However, it jumps at the interface between different media. This discontinuity can significantly reduce the order of accuracy of the numerical scheme. We solve the Maxwell equations, with an interface between two media, using a fourth-order accurate algorithm. We regularize the discontinuous dielectric permittivity by a continuous function either locally, near the interface, or globally, in the entire domain. We study the effect of this regularization on the order of accuracy for a one-dimensional time-dependent problem. We then implement this for the three-dimensional Maxwell equations in spherical coordinates with appropriate physical and arti- ficial absorbing boundary conditions. We use Fourier filtering of the high frequency modes near the poles to increase the time-step. Ó 2006 Elsevier Inc. All rights reserved. Keywords: CEM; FDTD; Discontinuous coefficients; High-order methods; Time-dependent Maxwell equations; High-order accuracy; Discontinuities 1. Introduction Electromagnetic waves propagate in both free space and in bodies, which may be inhomogeneous media. For instance, a cellular phone sends signals from a building to the closest antenna to register its location. Another example is a sensor that emits electromagnetic pulses into the ground to check for land mines. These can be simulated by the solution of Maxwell’s equations with discontinuous coefficients. A discontinuity in coefficients occurs at an interface between media with different dielectric and magnetic properties. The Maxwell equations for ~ E, ~ D, ~ H and ~ B are: 0021-9991/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2006.03.009 * Corresponding author. E-mail addresses: ekashdan@dam.brown.edu (E. Kashdan), turkel@post.tau.ac.il, turkel@math.tau.ac.il (E. Turkel). 1 Presently at Brown University. Journal of Computational Physics xxx (2006) xxx–xxx www.elsevier.com/locate/jcp ARTICLE IN PRESS