This study proposes a two-and-a-half-dimensional (2.5D) singular boundary method (SBM) to solve three dimensional (3D) acoustic problems with a constant cross section excited by harmonic point sources. The SBM expands the solution of a problem with a linear combination of fundamental solutions of the governing equation. The singular terms in the fundamental solutions are replaced by the origin intensity factors (OIFs). Nevertheless, the SBM suffers quadratically increasing memory consumption and operation count with respect to the degree of freedoms owing to the fully-populated coefficient matrices. This makes the SBM not applicable in road and rail traffic systems, where the domain of interest always is a few hundred meters long. Taking advantage of the invariant cross section in these problems, the 2.5D method is devised to decompose the 3D problem into a summation of a set of simpler 2D problems, and thus enables the SBM to solve 3D traffic acoustic problems. To recast the results of 3D problems, a new formulation for numerical integration is proposed. The proposed 2.5D SBM is tested to two problems in both full-space and half-space to illustrate its effectiveness and feasibility.

这项研究提出了一种二维半（2.5D）奇异边界方法（SBM），以解决由谐波点源激发的具有恒定横截面的三维（3D）声学问题。SBM通过控制方程基本解的线性组合扩展了问题的解。基本解中的单数项被起点强度因子（OIF）代替。然而，由于完全填充的系数矩阵，相对于自由度，SBM遭受二次增加的存储器消耗和操作计数。这使得SBM不适用于道路和铁路交通系统，在该系统中，关注域始终长几百米。利用这些问题中不变的横截面，2。设计了5D方法将3D问题分解为一组更简单的2D问题的总和，从而使SBM能够解决3D交通声学问题。为了重铸3D问题的结果，提出了一种新的数值积分公式。拟议的2.5D SBM在全空间和半空间中都针对两个问题进行了测试，以说明其有效性和可行性。