On the BEM for acoustic wave problems

Abstract The progress of the boundary element method (BEM) for solving acoustic wave problems is reviewed in this paper. The BEM is in a unique position among all the numerical methods available for solving acoustic wave problems. During the last few decades, research on the acoustic BEM has overcome many of the difficulties, and it is now an accurate and efficient numerical method in modeling many large-scale acoustic problems. This paper focuses on reviewing the dual boundary integral equation (BIE) formulation pioneered by Burton and Miller, treatment of the singular integrals involved in the BIEs, discretization considerations, and fast solution methods for solving the acoustic BEM equations. New directions in the research on the acoustic BEM are also discussed, with a few examples to show the potentials of the BEM in modeling aeroacoustics, acoustic metamaterials, bioacoustics, and sound rendering in computer animations.