关键词: 声学, 梯度移动最小二乘加权, 有限元法, 数值方法

Abstract:

：It is well known that one key issue of analyzing acoustic problems using finite element method (FEM) is “numerical dispersion error” due to the “overly stiff” nature of the FEM. This will cause the accuracy deterioration in the solution when it comes to high wave number or irregular meshes. To overcome this problem, a gradient weighted by moving least-squares (GW-MLS) is presented for analyzing acoustic problem. The gradient of acoustic pressure is reconstructed by the weight function of moving least-squares (MLS). And this makes the GW-MLS model much softer than the “overly stiff” FEM model. In acoustic GW-MLS, the acoustic mass matrix and the vectors of boundary integrals are constructed by the standard FEM to insure the integral accuracy of the mass matrix and the boundary conditions applied on region boundary accurately. Numerical examples including a 2D tube model and car cavity model are presented. The results demonstrate that the GW-MLS reduces the numerical dispersion error effectively. And because of this, the GW-MLS achieves higher accuracy as compared with FEM when meshes are seriously distorted especially in calculating high wave number problems.

Key words: acoustic, finite element method, gradient weighted by moving least-squares, numerical method