An integral equation approach to three-dimensional acoustic radiation and scattering problems
An integral equation approach to three-dimensional acoustic radiation and scattering problems
复制标题
三维声辐射和散射问题的积分方程方法
DOI：
10.1121/1.1779751
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发表时间：
2004
影响因子：
2.4
通讯作者：
S. A. Yang
中科院分区：
文献类型：
--
作者：
S. A. Yang
本文给出了Krutitskii[IMA J.Appl]新近提出的边界积分方程法的数值实现和检验。数学课。，259-269(2000)]用于计算具有多个障碍物的诺依曼外问题中的三维声辐射和散射场。在障碍物内部引入一定边界条件的辅助边界，以消除虚设的特征频率。在所有边界上应用简单的源公式，得到一组具有弱奇异核的唯一可解积分方程组。为了便于数值实现，将修正后的积分方程组进一步变换为只含非奇异核的普通积分方程组。测试用例包括一个球体和一对相等球体的声辐射和散射。并与解析解和申克的主要方法进行了比较。数值结果证明了该方法的有效性、稳健性和准确性。
This paper provides numerical implementation and tests for a boundary integral equation method proposed recently by Krutitskii [IMA J. Appl. Math. 64, 259–269 (2000)] for evaluating three-dimensional acoustic radiation and scattering fields in the exterior Neumann problem for several obstacles. Auxiliary boundaries with certain prescribed boundary conditions are introduced inside the obstacles for the purpose of eliminating the fictitious characteristic frequencies. Applying the simple source formulation on all boundaries leads to a set of uniquely solvable integral equations with weakly singular kernels. To facilitate the numerical implementation, the modified integral equations are further transformed to ordinary ones that contain nonsingular kernels only. Test cases consist of the acoustic radiation and scattering by one sphere and a pair of equal spheres. Comparisons are made with analytical solutions and Schenck’s CHIEF method. Numerical results demonstrate the efficiency, robustness, and accuracy of...