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This paper presents a new fast multipole boundary element method (FM-BEM) forsolving the acoustic transmission problems in 2D periodic media. We divide theperiodic media into many fundamental blocks, and then construct the boundaryintegral equations in the fundamental block. The fast multipole algorithm isproposed for the square and hexagon periodic systems, the convergence of thealgorithm is analyzed. We then apply the proposed method to the acoustictransmission problems for liquid phononic crystals and derive the acoustic bandgaps of the phononic crystals. By comparing the results with those from planewave expansion method, we conclude that our method is efficient and accurate.

A periodic FM-BEM for solving the acoustic transmission problems in periodic media