求解外域辐射和散射声场的分形有限元方法

应用二级分形有限元方法计算了外域声场.用一人工边界把外域声场分为两部分,人工边界以内使用常规有限元方法,人工边界以外的无限大区域使用分形有限元方法.使用分形有限元方法,一方面形成几何自相似网格使得相邻层之间的单元刚度矩阵和质量矩阵具有非常简单的关系,另一方面引用自动满足无限远辐射条件的全域插值函数把节点自由度变换为一组广义坐标,因而计算量可以大大减少.数值计算结果表明:该方法对于计算无限大外域声场是有效的.

Fractal Finite Element Method for Exterior Sound Radiation and Scattering

The exterior acoustic problems are calculated by fractal finite element method. The infinite domain is divided into two parts by an artificial boundary,the conventional finite element method is adopted within the artificial boundary, and the fractal finite element method is employed in the outer region beyond the artificial boundary. The computer time can be reduced greatly by the fractal finite element method, because of the facts that the relationships of element matrix between the adjacent fractal layers are very simple and the node degrees of freedom are transformed into a set of general coordinates by using the global interpolation functions,which satisfy automatically Sommerfeld's radiation conditions. The numerical results show that this method is effective in solving exterior acoustics problems.