9 - Computational Electromagnetics: The Finite-Difference Time-Domain Method

Abstract

This chapter reviews key elements of the theoretical foundation and numerical implementation of finite-difference time-domain (FDTD) solutions of Maxwell's equations. FDTD and related space-grid time-domain techniques are direct solution methods for Maxwell's curl equations. These methods employ no potentials; rather they are based on volumetric sampling of the unknown electric and magnetic fields in and surrounding the structure of interest over a period of time. FDTD is one of the most powerful and widely used numerical modeling approaches for electromagnetic wave interaction problems. With expanding developer and user communities in an increasing number of disciplines in science and engineering, FDTD technology is continually evolving in terms of its theoretical basis, numerical implementation, and technological applications, which now span the spectral range from low-frequency (ELF) to daylight. FDTD and related techniques are marching-in-time procedures that simulate the continuous actual electromagnetic waves in a finite spatial region by sampled-data numerical analogs propagating in a computer data space. Time-stepping continues as the numerical wave analogs propagate in the space lattice to causally connect the physics of the modeled region. Predictive dynamic range is also focused in the chapter. For computational modeling of electromagnetic wave interaction structures using FDTD and related space-grid time-domain techniques, it is useful to consider the concept of a predictive dynamic range.