| 移动最小二乘配点的Petrov-Galerkin局部无网格方法 |
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| 引用本文： | 蒙彦宇,张健,关海爽,戴赫.移动最小二乘配点的Petrov-Galerkin局部无网格方法[J].北华大学学报(自然科学版),2007,8(4):362-368. |
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| 作者姓名： | 蒙彦宇 张健 关海爽 戴赫 |
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| 作者单位： | 北华大学,交通建筑工程学院,吉林,吉林,132013;北华大学,电气信息工程学院,吉林,吉林,132023;锦州市建设工程招投标办公室,辽宁,锦州,121000 |
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| 摘 要： | 基于加权残值法和移动最小二乘(MLS)法并结合局部Petrov-Galerkin无网格方法(MLPG)的灵活性,将移动最小二乘配点法应用到无网格方法当中,建立了MLS配点无网格法的基本方程.在局部子域上利用Petrov-Galerkin原理给出了微分方程局部弱形式,通过惩罚因子引入本质边界条件;将局部弱对称形式进行离散化后,推导出移动最小二乘配点的Petrov-Galerkin局部无网格系统的刚度矩阵、载荷矩阵.通过数值算例证明该方法具有很高精确性、有效性和实用性.
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| 关 键 词： | 无网格方法 加权残值法 移动最小二乘插值 局部Petrov-Galerkin法 |
| 文章编号： | 1009-4822（2007）04-0362-07 |
| 修稿时间： | 2007-03-28 |
Petrov-Galerkin Local Meshless Method of Moving Least Square Collocation |
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| MENG Yan-yu,ZHANG Jian,GUAN Hai-shuang,DAI He.Petrov-Galerkin Local Meshless Method of Moving Least Square Collocation[J].Journal of Beihua University(Natural Science),2007,8(4):362-368. |
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| Authors: | MENG Yan-yu ZHANG Jian GUAN Hai-shuang DAI He |
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| Abstract: | Based on the method of weighting residual value method and the Moving Least Square(MLS) and the flexibility of MLPG,the MLS collocation meshless method is used in meshless method and the fundamental equation of the MLS collocation meshless method is set up.In the local domain,the local weak symmetrical form is obtained by using Petrov-Galerkin theory and the boundary condition is essenced by penalty factor.The local weak symmetrical form is carried on the discretization,then the stiffness matrix and the load matrix of the system are inferred.Finally,the examples are applied to show the accurate,the validity and the practical applicability of this method. |
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| Keywords: | Meshless method Weighting residual value method Moving least square(MLS) interpolation Local Petrov-Galerkin method(MLPG) |
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