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Fast and Accurate Analysis of Complicated Metamaterial Structures Using a Low-Frequency Multilevel Fast Multipole Algorithm

We present efficient solutions of electromagnetics problems involving realistic metamaterial structures using a low-frequency multilevel fast multipole algorithm (LF-MLFMA). Ordinary implementations of MLFMA based on the diagonalization of the Green's function suffer from the low-frequency breakdown, and they become inefficient for the solution of metamaterial problems discretized with very small elements compared to the wavelength. We show that LF-MLFMA, which employs multipoles explicitly without diagonalization, significantly improves the solution of metamaterial problems in terms of both processing time and memory.