Novel implementation of multilevel fast multipole algorithm for higher-order Galerkin's method

Abstract

A new approach is proposed to enhance the efficiency and reduce the memory requirements of the multilevel fast multipole algorithm (MLFMA) when applied to the higher-order Galerkin's method. This approach represents higher-order basis functions by a set of point sources such that a matrix-vector multiply is equivalent to calculating the fields at a number of points from given current sources at these points. The MLFMA is then applied to calculate the point-to-point interactions. This permits the use of more levels in MLFMA than applying MLFMA to basis-to-basis interactions directly and thus reduces the memory requirements significantly.