Tong Mei Song, Chew Weng Cho, White Michael J
Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
J Acoust Soc Am. 2008 May;123(5):2513-21. doi: 10.1121/1.2897048.
The multilevel fast multipole algorithm (MLFMA) is extended to solve for acoustic wave scattering by very large objects with three-dimensional arbitrary shapes. Although the fast multipole method as the prototype of MLFMA was introduced to acoustics early, it has not been used to study acoustic problems with millions of unknowns. In this work, the MLFMA is applied to analyze the acoustic behavior for very large truncated ground with many trenches in order to investigate the approach for mitigating gun blast noise at proving grounds. The implementation of the MLFMA is based on the Nystrom method to create matrix equations for the acoustic boundary integral equation. As the Nystrom method has a simpler mechanism in the generation of far-interaction terms, which MLFMA acts on, the resulting scheme is more efficient than those based on the method of moments and the boundary element method (BEM). For near-interaction terms, the singular or near-singular integrals are evaluated using a robust technique, which differs from that in BEM. Due to the enhanced efficiency, the MLFMA can rapidly solve acoustic wave scattering problems with more than two million unknowns on workstations without involving parallel algorithms. Numerical examples are used to demonstrate the performance of the MLFMA with report of consumed CPU time and memory usage.
多级快速多极子算法（MLFMA）被扩展用于求解具有三维任意形状的超大物体的声波散射问题。尽管作为MLFMA原型的快速多极子方法很早就被引入声学领域，但它尚未被用于研究具有数百万未知数的声学问题。在这项工作中，MLFMA被应用于分析具有许多沟槽的超大截断地面的声学行为，以研究在试验场减轻枪炮爆炸噪声的方法。MLFMA的实现基于Nystrom方法来创建声学边界积分方程的矩阵方程。由于Nystrom方法在生成MLFMA所作用的远相互作用项时机制更简单，因此所得方案比基于矩量法和边界元法（BEM）的方案更高效。对于近相互作用项，使用一种稳健技术来评估奇异或近奇异积分，这与BEM中的技术不同。由于效率提高，MLFMA可以在不涉及并行算法的情况下，在工作站上快速求解具有超过两百万个未知数的声波散射问题。数值例子用于展示MLFMA的性能，并报告所消耗的CPU时间和内存使用情况。
