Marching‐on‐in‐degree solution of volume integral equations for analysis of transient electromagnetic scattering by inhomogeneous dielectric bodies with conduction loss

Abstract

AbstractA time‐domain volume integral equation (TDVIE) solved by the marching‐on‐in‐degree (MOD) scheme is presented for the analysis of transient electromagentic scattering from a three‐dimensional inhomogeneous dielectric object of arbitrary shape with conduction loss.The volume of the object is discretized into curvilinear hexahedral elements, and conformal basis functions are utilized to expand the spatial variation of the electric flux density in the TDVIE. The transient variation of the electric flux density is expressed in term of weighted Laguerre polynomials so that the first, second, and third temporal derivatives of the electric flux density can be handled analytically. By applying the Galerkin spatial and temporal testing procedure, the TDVIE is converted into a recursive matrix equation in terms of the orders of the weighted Laguerre polynomials. Because of the elimination of the time variable in the MOD scheme, the proposed algorithm overcomes the late‐time instability problem that often occur in the conventional marching‐in‐on‐time (MOT) approach. Numerical results are presented to illustrate the good performance of the TDVIE algorithm. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1104–1109, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25897