多联通封闭空间声场响应的基于核重构的最小二乘无网格解法

针对多通域封闭空间声场响应的亥姆霍兹方程的求解问题，本文基于核重构思想，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。边界问题以及稳定性问题一直是无网格法的难点，该方法的系数矩阵是对称正定的，因此结果具有较好的稳定性。通过数值算例分析多联通域二维问题中配点均匀分布与随机分布时此方法的精确性以及稳定性，利用典型算例对比无网格方法数值解与解析解，结果证明此方法不需要进行网格划分，节点可随机分布，精度较高且具有良好的收敛性。

Acoustic response in multi-domain based on least-square point collocation method and reproducing kernel particle method

Meshless method faces several challenges,such as,boundary problems and stability of results.Here,approximated functions were constructed based on the principle of the reproducing kernel particle method and the least-square point collocation method was used to solve boundary problems.The system coefficient matrix generated with these methods was symmetric to ensure the results were stable.A least-square collocation formulation based on the reproducing kernel particle method was established for solving multi-domain acoustic response.Helmholtz equation was then discretized.To verify the proposed method,several numerical examples of two-dimensional problems were analyzed.Compared to analytic solutions to two examples,their numerical solutions computed with this meshless method were valid.This method did not need any initial mesh generation and mesh regeneration.Examples showed no matter how the points are distributed,uniformly or randomly,the results have good accuracy and convergence.