三维声场边界元法几乎奇异积分问题分析

以三维声场问题为例，提出一种准确计算高阶单元几乎奇异积分的半解析算法.首先分析高阶单元几何特征，构造近似几何量，然后应用扣除法，将奇异积分核函数分解为规则核函数与近似几何量表达的奇异核函数.规则核函数积分采用常规Gauss数值积分计算，奇异核函数积分采用半解析算法计算.给出三维声场内问题和外问题经典算例，计算了近边界点的声压，结果证明本文半解析算法的有效性和准确性.

Analysis of Nearly Singular Integral Problem in 3D Acoustic Field Boundary Element Method

Taking 3D acoustic analysis as an example, a semi-analytic algorithm is proposed which can be used to compute nearly singular integrals with high order element exactly. With analysis of geometry features of high order elements, approximate geometric parameters are constructed. Then, a kernel function of nearly singular integral is decomposed into two parts using subtraction method. One is regular part and the other is singular part. Integral of regular part is computed accurately using conventional Gauss quadrature. For integral of the singular part, semi-analytic algorithm gives exact result. Classical examples are given including 3D acoustic internal and external problems. Sound pressures at points near boundary are calculated with different methods. Comparisons of results demonstrate accuracy and effectiveness of the algorithm.