Improved Interpolation of Evanescent Plane Waves for Fast Multipole Methods

One way to implement a low-frequency or broadband fast multipole method is to use the spectral representation, or inhomogeneous plane-wave expansion, of the Green’s function. To significantly improve the error-controllability of the method, we propose a new interpolation and anterpolation scheme for the evanescent part. DOI: 10.2529/PIERS060907051636 The fast multipole method (FMM) can be used to accelerate the iterative solution of integral equations in electromagnetics and acoustics. In particular, the multilevel fast multipole algorithm (MLFMA) by Chew et al., is very efficient for solving large scale electromagnetic scattering problems [1]. However, the dynamic FMM and MLFMA are based on a plane-wave expansion of the Green’s function that is not error-controllable in the sub-wavelength scale. To implement a stable FMM in the sub-wavelength scale, there is basically two different approaches: either based multipole-series [2–4]; or based on a low-frequency stable inhomogeneous plane-wave expansion of the Green’s function [5–8]. The spectral representation of the Green’s function, G(r) = eikr 4πr = ik 8π2 π ∫