Helmholtz声学边界积分方程中奇异积分的计算

Calculation of Singular Integral for Helmholtz Boundary Integral Equation in Acoustics

提出了一种非等参单元的四边形坐标变换,它将积分的曲面单元映射为另一四边形单元,通过两次坐标变换引入的雅可比行列式可以消除Helmholtz声学边界积分方程中的弱奇异型O(1/r))积分,而且利用?r/?n以及坐标变换可以同时消除坐标变换无法消除的Cauchy型(O(1/r2))奇异积分,并给出了消除奇异性的详细证明,该方法给Helmholtz声学边界积分方程中的弱奇异积分与Cauchy奇异积分的计算以及编程提供了极大便利。

This paper presents a non- isoparametric transformatio n which can transformation surface to cube, the singularity (O(1/r)) will eliminated by coordinate transformation twice. Simultaneously, the Cauchy singularity (O(1/r22)) also can be eliminated via coord inate transformation and calculation of?r/?n, and the proving process is given in this paper in details. The method presented by this paper provides us a very simple way to computer the singular integral of Helmholtz boundary integral equation and to program in computer.