一种求解三维声腔声压分布问题的无网格法

利用传统有限元法求解声压分布问题常常受到污染误差和色散误差的困扰。加权最小二乘无网格法（MWLS）是一种基于移动最小二乘（MLS）近似的无网格方法，求解声腔声压分布问题具有低色散、高精度的特点。然而传统的MLS近似有时容易产生病态矩阵，利用加权正交基函数构建改进的移动最小二乘（IMLS）近似，得到的系统方程为非病态的。本文基于改进的加权最小二乘无网格法（IMWLS）求解三维声腔内部声压分布。计算得到的声压分布和声压频响曲线都与参考值十分吻合，峰值误差和污染误差都比FEM的小，计算成本相比无单元伽辽金法显著降低。计算结果表明IMWLS相比传统的FEM，能在更高的频段内达到高精度，并且相比EFGM能大幅提高计算效率。

A meshless method for solving the 3D sound pressure distribution problem

The traditional FEM suffers from pollution and dispersion phenomena when it was used to compute sound pressure distribution problem. The meshless weighted least-square (MWLS) method is a meshless method based on the moving least- square (MLS) approximation, which has Low dispersion, high precision characteristics with solving the problem of sound pressure distribution problem. The MLS may form ill-conditioned system of equations, an accurate solution of which is difficult to obtain. In this paper, by using the weighted orthogonal basis function to construct the improved moving least-square (IMLS) approximation, we derive the formulas and perform the dispersion analysis for an improved meshless weighted least- square (IMWLS) method for three-dimensional (3D) sound pressure distribution problem. Results demonstrated that the pressure distribution and the sound pressure frequency response curve of the calculated reference values agreed very well. The error of peak and pollution are smaller than FEM. The computational cost compared with the element free Galerkin method significantly reduced Results demonstrated that the proposed method can easily reach higher frequency without losing accuracy.