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

TL;DR

This paper introduces a fast multipole boundary element method tailored for 2D periodic media, enabling efficient and accurate analysis of acoustic transmission and band gaps in phononic crystals.

Contribution

The paper develops a novel FM-BEM approach for periodic media, including convergence analysis and application to phononic crystal band gap computation.

Findings

The method accurately predicts acoustic band gaps in liquid phononic crystals.

The FM-BEM demonstrates high efficiency compared to traditional methods.

Results agree well with plane wave expansion method.

Abstract

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.