A 3-DIMENSIONAL FDTD ALGORITHM IN CURVILINEAR COORDINATES

The finite-difference time-domain (FDTD) algorithm for the solution of electromagnetic scattering problems is formulated in numerically defined generalized coordinates in three dimensions and implemented in a code with the lowest order Bayliss-Turkel radiation boundary condition expressed in spherical coordinates. It is shown that the algorithm is capable of accurately tracking the progress of a pulse of electromagnetic radiation through the curvilinear mesh generated by a body of revolution, the only problems occurring in the vicinity of the rotation axis, which represents a coordinate singularity. A simple method to deal with this singular line is presented and discussed, and it is shown that, at least for our test problem, this approximation is sufficient. The algorithm discussed here is useful for the solution of the exterior problem in the presence of conductors and dielectrics having complicated shapes and electrical compositions, and for near-field problems such as cavity penetration problems. The far fields are obtained by replacing the scatterer with a virtual surface enclosing all sources. The (known) tangential fields on this surface are used in the evaluation of the Kirchhoff retarded-time integral, and scattering cross sections are then calculated at one backscatter angle as a function of frequency by Fourier transforming the scattered field. For the perfectly conducting test object used in this study, the backscatter cross section thus obtained agreed with moment method (MM) results over a limited frequency range, corresponding to wavelengths ranging roughly from eight to 20 times the largest grid dimension.