基于重构核的最小二乘配点法求解封闭声腔响应

Analysis of acoustic response in closed cavity based on least-square point collocation method and kernel reproducing particle method

基于重构核思想,应用无网格配点法构造近似函数,并利用最小二乘方法的原理解决边界问题,离散控制微分方程,建立求解的代数方程。并将此方法应用于封闭声腔响应的求解,即对亥姆霍兹方程进行离散,建立其最小二乘无网格配点格式。该方法的系数矩阵是对称正定的,因而保证了解的稳定性。通过数值算例分别验证了配点均匀分布与随机分布时此方法的精确性以及稳定性。与有限元方法相比较,此方法不需要进行网格划分,节点可随机分布,且随着节点数目的增加,其精度越来越高,并具有良好的收敛性。

In this paper,approximate functions are constructed based on the principle of reproducing kernel particle method,and the least-square collocation method is used to solve boundary problems.The system coefficient matrix generated by this method is symmetric,which make sure of the results stable.A least-square collocation formulation based on kernel reproducing particle method is established for solving acoustic response in closed cavity.Helmholtz equation is then discretized.Several numerical examples of points distributed uniformly or randomly are analyzed.Compared with FEM,this method dose not need any initial mesh generation and mesh regeneration.Examples show whenever the points are distributed uniformly or randomly the results have good accuracy and convergence.