FDTD simulation of EM wave propagation in 3-D media

Abstract

A finite‐difference, time‐domain solution to Maxwell’s equations has been developed for simulating electromagnetic wave propagation in 3-D media. The algorithm allows arbitrary electrical conductivity and permittivity variations within a model. The staggered grid technique of Yee is used to sample the fields. A new optimized second‐order difference scheme is designed to approximate the spatial derivatives. Like the conventional fourth‐order difference scheme, the optimized second‐order scheme needs four discrete values to calculate a single derivative. However, the optimized scheme is accurate over a wider wavenumber range. Compared to the fourth‐order scheme, the optimized scheme imposes stricter limitations on the time step sizes but allows coarser grids. The net effect is that the optimized scheme is more efficient in terms of computation time and memory requirement than the fourth‐order scheme. The temporal derivatives are approximated by second‐order central differences throughout. The Liao transmitting boundary conditions are used to truncate an open problem. A reflection coefficient analysis shows that this transmitting boundary condition works very well. However, it is subject to instability. A method that can be easily implemented is proposed to stabilize the boundary condition. The finite‐difference solution is compared to closed‐form solutions for conducting and nonconducting whole spaces and to an integral‐equation solution for a 3-D body in a homogeneous half‐space. In all cases, the finite‐difference solutions are in good agreement with the other solutions. Finally, the use of the algorithm is demonstrated with a 3-D model. Numerical results show that both the magnetic field response and electric field response can be useful for shallow‐depth and small‐scale investigations.