FDTD SIMULATION OF EM WAVE-PROPAGATION IN 3-D MEDIA

A finite-difference, time-domain solution to Maxwell's equations has b een developed for simulating electromagnetic wave propagation in 3-D m edia. The algorithm allows arbitrary electrical conductivity and permi ttivity 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 c onventional fourth-order difference scheme, the optimized second-order scheme needs four discrete values to calculate a single derivative. H owever, the optimized scheme is accurate over a wider wavenumber range . Compared to the fourth-order scheme, the optimized scheme imposes st ricter limitations on the time step sizes but allows coarser grids. Th e net effect is that the optimized scheme is more efficient in terms o f computation time and memory requirement than the fourth-order scheme . The temporal derivatives are approximated by second-order central di fferences throughout. The Liao transmitting boundary conditions are us ed to truncate an open problem. A reflection coefficient analysis show s 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 nonc onducting 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 resu lts show that both the magnetic field response and electric field resp onse can be useful for shallow-depth and small-scale investigations.