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

李鸿秋;陈国平;史宝军

振动与冲击 ›› 2012, Vol. 31 ›› Issue (8) : 148-152,.

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PDF(1530 KB)
振动与冲击 ›› 2012, Vol. 31 ›› Issue (8) : 148-152,.
论文

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

  • 李鸿秋1,2; 陈国平2; 史宝军3
作者信息 +

Acoustic Response in Multi-Domain Based on Least-Square Point Collocation Method and Reproducing Kernel Particle Method

  • Li Hong-qiu1; Chen Guo-ping 1; Shi Bao-jun 2
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文章历史 +

摘要

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。

Abstract

Meshless method faces several challenges such as boundary problems and stability of the results. In this paper, approximated functions were constructed based on the principle of reproducing kernel particle method and least-square collocation method was used to solve boundary problems. The system coefficient matrix generated by this method is symmetric, which make sure the results stable. A least-square collocation formulation based on kernel reproducing 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 of two examples, the numerical solutions computed by this meshless method are valid. This method needn’t any initial mesh generation and mesh regeneration. Examples show whenever the points were distributed uniformly or randomly the results have good accuracy and convergence.

关键词

声响应 / 多通域 / 亥姆霍兹方程 / 重构核配点法 / 最小二乘原理

Key words

Acoustic response / multi-domain / Helmholtz equation / reproducing kernel particle method / least-square principle

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导出引用
李鸿秋;陈国平;史宝军. 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[J]. 振动与冲击, 2012, 31(8): 148-152,
Li Hong-qiu;Chen Guo-ping;Shi Bao-jun . Acoustic Response in Multi-Domain Based on Least-Square Point Collocation Method and Reproducing Kernel Particle Method[J]. Journal of Vibration and Shock, 2012, 31(8): 148-152,

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