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