A wideband fast integral equation solver combining multilevel fast multipole and multilevel Green's function interpolation method with fast Fourier transform acceleration

Abstract

A wideband fast integral solver employing a fast Fourier transform accelerated multilevel Green's function interpolation method (MLIPFFT) combined with the multilevel fast multipole method (MLFMM) is presented. On fine levels of the employed oct-tree structure, the low frequency stable MLIPFFT is utilized. At a certain wavelength dependent threshold for the box size, the interpolation point based representation of the MLIPFFT is converted into its k-space representation suitable for an MLFMM. On the coarser levels, MLFMM translations are used then, where the MLIPFFT becomes less efficient. The functionality of this hybrid algorithm is demonstrated in an example.