Combined multilevel FMM-QR algorithm for broadband applications

Abstract

This paper presents a combined multilevel FMM-QR approach applicable to three-dimensional scattering problems of widely varying electrical sizes. The classic MLFMA suffers breakdown at low frequencies (I. Bogaert et al., 2005), while QR based methods become inefficient at high frequencies (D. Gope and V. Jandhyala, 2005). The presented algorithm combines these two methods to achieve stability at all frequencies, and at the same time preserves the O(NlogN) complexity of setup, memory and matrix-vector products. Examples demonstrating time and memory requirements are presented, and the efficient nature of the overall method at all frequencies is also demonstrated