A three-dimensional FDTD algorithm in curvilinear coordinates [EM scattering]

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 its is shown that, at least for the test problem, this approximation is sufficient. The algorithm discussed is useful for the solution of the exterior problem in the presence of conductors and dielectrics with 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