Finite-difference time-domain simulations of wave propagation and scattering as a research and educational tool

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Abstract
In this article we introduce the finite‐difference time‐domain (FDTD) method to solve the wave equation. The FDTD algorithm is a useful tool to study wave propagation and scattering processes because the wave fields, which are computed at each time step, can be displayed to produce animated visualizations during the computation. The FDTD algorithm is simple to implement, easily parallelizable, and well suited to solving wave propagation and scattering problems with complicated boundaries and nonuniform media. In the FORTRAN 90 programming language the basic code is only a few lines, and the computation time is independent of problem complexity. In this article we derive the basic FDTD algorithm and reinterpret it in terms of an interacting cell model and heuristically derive various features that normally require detailed analysis. Finally we show how to implement boundary conditions at the subgrid level.

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