A broadband multilevel fast multipole algorithm with incomplete-leaf tree structures for multiscale electromagnetic problems

Abstract

An efficient, broadband, and accurate multilevel fast multipole algorithm (MLFMA) is proposed to solve a wide range of multiscale electromagnetic problems with orders of magnitude differences in the mesh sizes. Given a maximum RWG population threshold, only overcrowded boxes are recursively bisected into smaller ones, which leads to novel incomplete-leaf tree structures. Simulations reveal that, for surface discretizations possessing highly overmeshed local regions, the proposed method presents a more efficient and/or accurate results than the conventional MLFMA. The key feature of such a population-based clustering scenario is that the error is controllable, and hence, regardless of the number of levels, the efficiency can be optimized based on the population threshold. Numerical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison to the conventional MLFMA.