Abstract:

In order to improve the computational efficiency for half space acoustic problems, a half space Green function was introduced in boundary integral equations, then the multipole Galerkin boundary element method (BEM) was used to solve the half space acoustic problems. During this process, the matrix-vector multiplication procedure was discussed, and the generalized minimal RESidual (GMRES) iterative solver pre-conditioned by approximate inverse method was employed to solve the system linear equations. The numerical results show that, the accuracy and efficiency of the multipole Galerkin BEM is validated by the half space monopole scattering problem. The approximate inverse pre-conditioner can accelerate the convergence rate of the GMRES solver, the iterative steps are reduced dramatically. Finally, the multipole Galerkin BEM was applied to solve the diffraction problem of two dimensional T shape noise barrier.

Key words: Galerkin boundary element method, fast multipole method, half space problem, acoustics;numerical calculation

摘要：

为提高求解半空间声学问题的计算效率，将半空间格林公式引入到边界积分方程中，使用伽辽金多极边界元法求解了二维半空间声学问题。在求解半空间问题时，推导了伽辽金多极算法中矩阵向量乘积的实现过程;在求解系统线性方程组时，使用近似求逆方法对系统系数矩阵进行了预处理。数值计算结果表明：二维半空间点声源声辐射算例有效地验证了半空间伽辽金多极边界元法计算精度;与全空间镜像方法计算时间对比结果表明，半空间方法具有更高的计算效率;在求解经过近似求逆预处理的系统方程时，迭代步数显著减少了，加速了迭代求解器的收敛。最后，使用半空间的伽辽金多极边界元法求解了T形声屏障声散射问题。

关键词: 伽辽金边界元法, 快速多极方法, 半空间问题, 声学, 数值计算