Electromagnetic Computation Methods for Lightning Surge Protection Studies

3The Finite-Difference Time Domain Method for Solving Maxwell’s Equations

3.1 Introduction

The finite-difference time domain (FDTD) method (Yee 1966) is one of the most widely used electromagnetic computation methods for a variety of electromagnetic problems. The FDTD method uses the central difference approximation to Maxwell’s curl equations, which are Faraday’s law and Ampere’s law, in the time domain. Gauss’s law is also satisfied. The method solves the resultant update equations for electric and magnetic fields at each time step and at each discretized space point in the working volume using the leapfrog method. For the analysis of the electromagnetic response of a structure in an unbounded space, an absorbing boundary condition such as Liao’s condition (Liao et al. 1984) or perfectly matched layers (Berenger 1994), which both suppress unwanted reflections, needs to be applied. Advantages of the FDTD method in comparison with other electromagnetic computation methods can be summarized as follows:

1. It is based on a simple procedure, and therefore its computer programming is relatively easy.
2. It is capable of treating complex geometries and inhomogeneities.
3. It is capable of incorporating nonlinear effects and components.
4. It can handle wideband quantities from one run with a time-to-frequency transforming tool.

Its disadvantages are:

1. It is computationally expensive compared to other methods such as the method of moments (MoM).
2. It cannot deal with oblique boundaries that ...