A Time-Domain, Finite-Volume Treatment for the Maxwell Equations

Abstract

For computation of electromagnetic scattering from layered objects, the differential form of the time-domain Maxwell's equations are first cast in a conservation form and then solved using a finite-volume discretization procedure derived from proven Computational Fluid Dynamics (CFD) methods ¹ Shankar , V. , Chajtravarthy , S. , and Szema , K.-Y. , “ Development and Application of CFD Methods to Problems in Computational Science ,”, March 7 — 11 , 1988 , University of Tennessee Space Institute , Tullahoma , Tennessee . [Google Scholar] . The formulation accounts for any variations in the material properties (time, space, and frequency dependent), and can handle thin resistive sheets and lossy coatings by positioning them at finite-volume cell boundaries. The time-domain approach handles both continuous wave (single frequency) and pulse (broadband frequency) incident excitation. Arbitrarily shaped objects are modeled by using a body-fitted coordinate transformation. For treatment of complex internal/external structures with many material layers, a multizone framework with ability to handle any type of zonal boundary conditions (perfectly conducting, flux through, zero flux, periodic, nonreflecting outer boundary, resistive card, and lossy coatings, etc.) is implemented. The finite—volume procedure employs an explicit Lax-Wendroff upwind scheme to integrate Maxwell's equations in time. The time—domain electromagnetic field values are converted to the frequency domain using fast Fourier transforms (FFT), and then a Green's function based near field-to-far field transformation is employed to obtain the bistatic radar cross section (RCS).