Plane-wave time-domain accelerated radiation boundary kernels for FDTD analysis of 3-D electromagnetic phenomena

Truncating finite difference time domain meshes using exact radiation boundary conditions is computationally expensive. The computational bottleneck stems from the global nature of the resulting boundary update scheme, which calls for the evaluation of retarded-time boundary integrals at each time step. The classical evaluation of such integrals requires O(N_s²) operations per time step where N_s is the number of spatial field sampling points on the boundary. Here, the plane wave time domain algorithm is used to evaluate retarded-time boundary integrals in O(N_slog²N_s) operations per time step and thereby accelerate finite difference time domain solvers that impose exact radiation boundary conditions. The effectiveness of the resulting approach and its computational complexity are demonstrated through several numerical examples.