A local filtering scheme for FMM/PWTD algorithms

Accurate and efficient schemes for interpolating and filtering/anterpolating far field radiation patterns are key to the operation of the multilevel fast multipole method (FMM) (Song, J.M. et al., IEEE Trans. Antennas and Propag., vol.45, p.1488-93, 1997) and plane wave time domain (PWTD) (Shanker, B. et al., IEEE Trans. Antennas and Propag., vol.51, 2003) accelerated frequency and time domain integral equation solvers. Local interpolators and filters/anterpolators, like those used by Song et al., offer distinct advantages over their global counterparts (Shanker et al., 2003; Sarvas, J., 2002), especially in parallel implementations. We propose a simple local filtering scheme suitable for incorporation into FMM and PWTD field evaluation kernels. The filter relies on periodic approximate prolate spheroidal (APS) functions (Bucci, O.M. et al., 1991) to restrict coupling among radiation directions. A numerical example shows that the error due to the proposed local filtering scheme decays exponentially fast with respect to the oversampling and "time-bandwidth" factors that define the periodic APS function and can be made arbitrarily small.