关键词: Helmholtz方程, 边界元方法, 大规模, 快速多极算法, 声学

Abstract: In order to overcome the difficulty of the conventional boundary element method (BEM) is unsuitable for solving large-scale acoustic simulations, the fast multipole method (FMM) is used with the conventional BEM for solving large-scale acoustic problems. The computational efficiency of the fast multipole BEM (FMBEM) is improved significantly compared to the conventional BEM due to the multipole expansion of the fundamental solution and using the preconditioned generalized minimum residual method (GMRES) as an iterative solver to solve system of linear equation. Thus, both the computational complexity and memory requirement of the present FMBEM are drastically reduced to O(N), where N is the number of degrees of freedom. In order to remove the non-unique problems of the conventional BEM, the FMBEM employs the improved Burton-Miller method to solve the exterior acoustic problems for all frequencies. Numerical examples validate the accuracy of the FMBEM, and show that the present algorithm provides an order of magnitude increase in computational efficiency compared to the conventional BEM. These examples clearly demonstrate that the present FMBEM is effective to solve large-scale acoustic problems.

Key words: Acoustic problems, Boundary element method, Fast multipole method, Helmholtz equation, Large-scale