Fast and accurate analysis of large metamaterial structures using the multilevel fast multipole algorithm

Date
2009
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Source Title
Progress in Electromagnetics Research
Print ISSN
1070-4698
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Volume
95
Issue
Pages
179 - 198
Language
English
Type
Article
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Abstract

We report fast and accurate simulations of metamaterial structures constructed with large numbers of unit cells containing split-ring resonators and thin wires. Scattering problems involving various metamaterial walls are formulated rigorously using the electric-field integral equation, discretized with the Rao-Wilton-Glisson basis functions. Resulting dense matrix equations are solved iteratively, where the matrix-vector multiplications are performed efficiently with the multilevel fast multipole algorithm. For rapid solutions at resonance frequencies, convergence of the iterations is accelerated by using robust preconditioning techniques, such as the sparse-approximate-inverse preconditioner. Without resorting to homogenization approximations and periodicity assumptions, we are able to obtain accurate solutions of realistic metamaterial problems discretized with millions of unknowns.

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Keywords
Accurate analysis, Dense matrices, Fast and accurate simulations, Homogenization approximation, Matrix vector multiplication, Metamaterial structures, Multi-level fast multi-pole algorithm, Preconditioners, Preconditioning techniques, Rao-Wilton-Glisson basis functions, Scattering problems, Split-ring resonator, Thin wires, Unit cells, Resonance, Metamaterials
Citation
Published Version (Please cite this version)