Abstract

This paper presents a new fast multipole boundary element method (FM-BEM) for solving the acoustic transmission problems in 2-D periodic media. We divide the periodic media into fundamental blocks, and then construct the boundary integral equations in the fundamental block. The fast multipole algorithm is proposed for the square periodic and hexagonal periodic structures, the convergence and complexity of the algorithm are analyzed. Our approach is applied to solve the acoustic transmission problems for liquid phononic crystals, the acoustic band gaps of the phononic crystals are derived.

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