Fast solution of finite element/boundary integral problems employing hierarchical Green's function interpolation combined with multilevel fast multipole method

Abstract

A fast solver for finite element/boundary integral (FEBI) problems is discussed, which is suitable for low frequency as well as mid frequency problems. For the boundary integral part, low frequency computations are approximated by multilevel Green's function interpolation with fast Fourier transform acceleration (MLIPFFT). Mid frequency computations are accelerated by the multilevel fast multipole method (MLFMM). Furthermore, hierarchical and nearly-orthogonal higher order basis functions are considered as well as a loop-tree decomposition of Rao-Wilton-Glisson (RWG) basis functions. In numerical examples, the efficiency of the combined MLIPFFT/MLFMM fast solver is shown.