Efficient Solutions of Metamaterial Problems Using a Low-Frequency Multilevel Fast Multipole Algorithm

Abstract

Abstract-We present fast and accurate solutions of electromagnetics problems involving realistic metamaterial structures using a lowfrequency multilevel fast multipole algorithm (LF-MLFMA). Accelerating iterative solutions using robust preconditioning techniques may not be sufficient to reduce the overall processing time when the ordinary high-frequency MLFMA is applied to metamaterial problems. The major bottleneck, i.e., the low-frequency breakdown, should be eliminated for efficient solutions. We show that the combination of an LF-MLFMA implementation based on the multipole expansion with the sparse-approximate-inverse preconditioner enables efficient and accurate analysis of realistic metamaterial structures. Using the robust LF-MLFMA implementation, we demonstrate how the transmission properties of metamaterial walls can be enhanced with randomlyoriented unit cells.

Fast and Accurate Analysis of Homogenized Metamaterials With the Surface Integral Equations and the Multilevel Fast Multipole Algorithm

“…Therefore, in addition to fast algorithms, preconditioning and stabilization techniques are required to ensure reliable solutions. Despite the challenging nature of the problems, some realistic metamaterials have been successfully analyzed via full-wave solvers, particularly those based on MLFMA [6], [7].…”

Comparison of Surface Integral Equations for Left-Handed Materials

“…Surface integral equations (SIE) have been extensively used for solving scattering problems involving homogeneous or piecewise homogeneous dielectric objects [8][9][10][11][12][13][14][15]. Recent works have shown that their application may be extended to the homogeneous LHM analysis [16][17][18][19].…”

Symmetric Inverse-Based Multilevel Ilu Preconditioning for Solving Dense Complex Non-Hermitian Systems in Electromagnetics

“…In recent years, a significant amount of work has been devoted to design fast parallel algorithms that can reduce the O (n 2 ) computational complexity for the M-V product with boundary element equations, like the Fast Multipole Method (FMM) by V. Rokhlin [35], the H-matrix approach by W. Hackbush [25], the Adaptive Cross Approximation by M. Bebendorf [4], and other approaches. Since the pioneering work by Rokhlin and his co-authors, the Fast Multipole Algorithm continues to receive considerable attention in Electromagnetics, see e.g., [20,21,31,32,39].…”