FDTD algorithm in curvilinear coordinates (EM scattering)

The finite-difference-time-domain (FDTD) algorithm for the solution of electromagnetic scattering problems is formulated in generalized coordinates in two dimensions and implemented in a code with the lowest-order Bayliss-Turkel radiation boundary condition expressed in cylindrical coordinates. It is shown that, for a perfect conductor, such a formulation leads to a stable, well-posed algorithm and that, in regions where the curvature of the coordinate lines is not great, the dispersion and anisotropy effects are negligible. Such effects become more pronounced in regions of high curvature, leading to unphysical phase shifts. The magnitude of such shifts and the amount of wavefront distortion is studied via numerical experiments using a cylindrical mesh. Near-field results are given for two canonical shapes for each polarization: the circular cylinder and cylinders of square and rectangular cross sections. These results are compared with those obtained by exact eigenfunction expansion techniques, with method-of-moments (MM) solutions, and with solutions obtained from an alternate FDTD approach. In each case, agreement is excellent. The propagation of a plane wave through a polar space in the absence of a scatterer is also examined, and it is shown that the FDTD algorithm is capable of tracking the incident wave closely.<
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