EFFICIENT SOLUTIONS OF METAMATERIAL PROBLEMS USING A LOW-FREQUENCY MULTILEVEL FAST MULTIPOLE ALGORITHM

We present fast and accurate solutions of electromagnet- ics problems involving realistic metamaterial structures using a low- frequency multilevel fast multipole algorithm (LF-MLFMA). Acceler- ating iterative solutions using robust preconditioning techniques may not be su-cient to reduce the overall processing time when the or- dinary high-frequency MLFMA is applied to metamaterial problems. The major bottleneck, i.e., the low-frequency breakdown, should be eliminated for e-cient solutions. We show that the combination of an LF-MLFMA implementation based on the multipole expansion with the sparse-approximate-inverse preconditioner enables e-cient and ac- curate analysis of realistic metamaterial structures. Using the robust LF-MLFMA implementation, we demonstrate how the transmission properties of metamaterial walls can be enhanced with randomly- oriented unit cells.