Meshless Galerkin least-squares method
Meshless Galerkin least-squares method
复制标题
无网格伽辽金最小二乘法
DOI：
10.1007/s00466-004-0615-8
复制
发表时间：
2005-02
影响因子：
4.1
通讯作者：
陆明万
中科院分区：
文献类型：
--
作者：
潘小飞;张雄;陆明万
配点法和伽辽金法是现有无网格法中的主要方法。基于Galerkin的无网格方法是计算密集型的，而基于配置的无网格方法遭受不稳定性。本文将Galerkin法和配点法的优点联合收割机结合起来，提出了一种新的高效无网格方法--无网格Galerkin最小二乘法。将问题域划分为内部域和边界域两个子域。在边界区域采用Galerkin方法，而在内部区域采用最小二乘法，避免了最小二乘法在边界条件不正确时出现伪解的可能性。为了验证该方法的精度和效率，对悬臂梁和含中心圆孔的无限大板进行了详细的数值分析，并与基于Galerkin的无网格法（GBMM）、基于配置的无网格法（CBMM）和无网格加权最小二乘法（MWLS）的计算结果进行了比较.数值研究表明，该方法的精度远高于CBMM，接近甚至优于GBMM，而计算量远小于GBMM.
Collocation method and Galerkin method have been dominant in the existing meshless methods. Galerkin-based meshless methods are computational intensive, whereas collocation-based meshless methods suffer from instability. A new efficient meshless method, meshless Galerkin lest-squares method (MGLS), is proposed in this paper to combine the advantages of Galerkin method and collocation method. The problem domain is divided into two subdomains, the interior domain and boundary domain. Galerkin method is applied in the boundary domain, whereas the least-squares method is applied in the interior domain.The proposed scheme elliminates the posibilities of spurious solutions as that in the least-square method if an incorrect boundary conditions are used. To investigate the accuracy and efficiency of the proposed method, a cantilevered beam and an infinite plate with a central circular hole are analyzed in detail and numerical results are compared with those obtained by Galerkin-based meshless method (GBMM), collocation-based meshless method (CBMM) and meshless weighted least squares method (MWLS). Numerical studies show that the accuracy of the proposed MGLS is much higher than that of CBMM and is close to, even better than, that of GBMM, while the computational cost is much less than that of GBMM.
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DOI：
10.1016/s0045-7825(03)00216-0
发表时间：
2003-04
影响因子：
7.2
作者：
Wen Chen;Y. Hon
通讯作者：
Wen Chen;Y. Hon
影响因子：
4.1
作者：
Jeng-Tzong Chen;M. Chang;K. Chen;I. Chen
通讯作者：
Jeng-Tzong Chen;M. Chang;K. Chen;I. Chen
DOI：
10.1016/s0955-7997(02)00017-6
发表时间：
2002-06
期刊：
ArXiv
影响因子：
--
作者：
Wen Chen
通讯作者：
Wen Chen
影响因子：
1.5
作者：
P. Jiang;Shu-Qing Li;C. Chan
通讯作者：
P. Jiang;Shu-Qing Li;C. Chan
DOI：
10.1002/(sici)1097-0207(19990930)46:3
发表时间：
1999-09
影响因子：
2.9
作者：
B. P. Patel;M. Ganapathi;J. Saravanan
通讯作者：
B. P. Patel;M. Ganapathi;J. Saravanan