非光滑结构表面声学边界元法中奇异积分计算方法

A New Method for Accurately Calculating Singular Integrals in Solving Helmholtz Boundary Integral Equation

提出了采用三角形或四边形改进的二次插值函数,并结合局部极坐标变换或引入退化单元的方法,解决了任意三维非光滑结构表面声学计算边界元法中的奇异积分问题。通过计算脉动球源和立方体的表面辐射声压,证明了方法的有效性和对任意非光滑结构表面的适应性,该方法具有精度高和收敛速度快的特点。

The method of Li et al can not calculate the singular integrals encountered in the Helmholtz boundary integral equation associated with sound radiation and scattering for arbitrary nonsmooth threedimensional bodies. We now present a new method that can do so. In the full paper, we explain in detail our new method; in this abstract, we just list the two topics of our explanation： （A） brief introduction to Helmholtz boundary integral equation; （13） accurate calculation of singular integrals; for the purpose of calculation, we derive eqs. （3） through （13） in the full paper; we employ the second-order interpolation functions proposed by Chien et al. It is perhaps worth mentioning that, although our accurate calculation includes the computation of potential kernels, no extra effort is really involved since these kernels are a subset of the kernels found in the acoustic problems. In order to demonstrate the robustness, accuracy and convergence of the proposed method, two numerical examples of sound radiation from a pulsating sphere （numerical results given in Table 1 of the full paper） and a cube （numerical results given in Table 2 of the full paper） are presented respectively. In both cases good agreement is obtained between the proposed method and closed-form solutions.