A multilevel interpolating fast integral solver with fast fourier transform acceleration

Abstract

A fast integral solution of the electric field integral equation employing multilevel Lagrange interpolation factorization of the free-space Green's function is presented. The multilevel interpolation representation works on the same oct-tree structure as it is common in the multilevel fast multipole methods. The drawback of the bad computational efficiency of the multilevel interpolation representation due to involved full translation operators is overcome by employing the Fast Fourier Transformation to achieve diagonalization. In a variety of examples, it is shown that this solver achieves excellent computation time and memory efficiencies. Even at very low frequencies it is possible to accelerate a not stabilized electric field integral equation solution which is known to be badly conditioned.