An O(NsNt log2Nt) TDIE solver for scattering from periodic quasiplanar domains

Transient analysis of periodic structures finds application in a number of areas in applied electromagnetics. The cost of these analyses scales as O(N_s²N_t²), where N_s and N_t are the number of spatial and temporal degrees of freedom. In this paper, we (1) present a method that reduces the cost of this evaluation to O(N_sN_t log² N_t) for quasiplanar structures and (2) integrate this into a late time stable TDIE solver. The method is based on an expansion of the Time Domain Floquet Wave Green´s Function in which the number of contributing Floquet modes is limited through the use of a band limited temporal basis function. Spatial acceleration is achieved using the method of Accelerated Cartesian Expansion and temporal acceleration using a block FFT scheme. Results are presented that validate the accuracy and scalability of the method.