In this paper, a numerical methodology based on a two-and-a-half-dimensional (2.5D) singular boundary method (SBM) to deal with acoustic radiation and scattering problems in the context of longitudinally invariant structures is proposed and studied. In the proposed 2.5D SBM, the desingularisation provided by the subtracting and adding-back technique is used to determine the origin intensity factors (OIFs). These OIFs are derived by means of the OIFs of the Laplace equation. The feasibility, validity and accuracy of the proposed method are demonstrated for three acoustic benchmark problems, in which detailed comparisons with analytical solutions, the 2.5D boundary element method (BEM) and the 2.5D method of fundamental solutions (MFS) are performed. As a novelty of the present study, it is found that the 2.5D SBM provides a higher numerical accuracy than the 2.5D linear-element BEM and lower than the 2.5D quadratic-element BEM. Although the results obtained depict that a nodal approximation of the boundary geometry leads to a significant reduction in the accuracy of the 2.5D SBM, the delivered errors are still acceptable. For complex geometries, the 2.5D SBM is found to be simpler and more robust than the 2.5D MFS, since no optimization procedure is required.

在本文中，提出并研究了一种基于二维半（2.5D）奇异边界法（SBM）的数值方法来处理纵向不变结构背景下的声辐射和散射问题。在提议的 2.5D SBM 中，减法和加法技术提供的去奇异化用于确定原始强度因子 (OIF)。这些 OIF 是通过拉普拉斯方程的 OIF 导出的。针对三个声学基准问题证明了该方法的可行性、有效性和准确性，其中与解析解、2.5D 边界元法 (BEM) 和 2.5D 基本解法 (MFS) 进行了详细比较。作为本研究的一个新颖之处，发现 2。5D SBM 提供比 2.5D 线性元 BEM 更高的数值精度，但低于 2.5D 二次元 BEM。尽管获得的结果表明边界几何的节点近似导致 2.5D SBM 的精度显着降低，但传递的误差仍然是可以接受的。对于复杂的几何形状，发现 2.5D SBM 比 2.5D MFS 更简单、更稳健，因为不需要优化程序。