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On the BEM for acoustic wave problems

机译：关于声波问题的边界元法

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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.
机译：本文综述了边界元法在解决声波问题上的研究进展。在解决声波问题的所有数值方法中，BEM都处于独特的位置。在过去的几十年中，对声学BEM的研究克服了许多困难，现在它已成为对许多大型声学问题进行建模的准确而有效的数值方法。本文着重研究Burton和Miller率先提出的对偶边界积分方程（BIE）公式，对BIE中涉及的奇异积分的处理，离散化注意事项以及用于求解声学BEM方程的快速求解方法。还讨论了声学BEM研究的新方向，并举例说明了BEM在模拟计算机声学中的航空声学，声学超材料，生物声学和声音渲染方面的潜力。

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