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IEFG针对矩形域内的Poisson方程的精确度研究
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作者 王丽萍 任红萍 《太原师范学院学报(自然科学版)》 2015年第1期1-4,共4页
在移动最小二乘插值法的基础上,对插值型无单元Galerkin方法(IEFG)在矩形域内的势问题的精确度进行研究.IEFG方法在运用于工程计算时,可以直接施加边界条件,具有计算简便精度高的优点.
关键词 无网格方法 移动最小二乘插值法 插值型无单元Galerkin方法(iefg) 权函数 形函数
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IEFG针对环形域内的Poisson方程的精确度研究
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作者 凌建国 王丽萍 《太原师范学院学报(自然科学版)》 2015年第2期17-20,共4页
基于移动最小二乘插值法的基础上,对提出的插值型无单元Galerkin方法(IEFG)在环形域内的势问题的精确度的研究.IEFG方法运用于工程计算时,可以直接施加边界条件,通过对误差进行分析表明,IEFG方法在运用于工程计算时,确实也提高了计算精度.
关键词 无网格方法 移动最小二乘法 插值型无单元Galerkin方法(iefg) 权函数 形函数
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改进型无网格伽辽金-有限元耦合法在三维立体区域热传导中的应用 被引量:1
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作者 赵玉凤 《东莞理工学院学报》 2020年第1期25-29,共5页
基于移动最小二乘近似的改进型无网格伽辽金法具有高精度、高效率且不会得到病态系统方程等优点,将改进型无网格伽辽金法和有限元法耦合,得到改进型无网格伽辽金-有限元耦合法,并利用这种新方法分析了三维稳态的导热问题。计算结果表明... 基于移动最小二乘近似的改进型无网格伽辽金法具有高精度、高效率且不会得到病态系统方程等优点,将改进型无网格伽辽金法和有限元法耦合,得到改进型无网格伽辽金-有限元耦合法,并利用这种新方法分析了三维稳态的导热问题。计算结果表明,该方法所得结果与精确解高度吻合,比耦合前的改进型无网格伽辽金法和有限元法的精度和效率更高。 展开更多
关键词 改进型无网格迦辽金法 有限元 温度场
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利用插值型无单元Galerkin方法求解KdV-B方程
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作者 裴凯燕 郭龙飞 任红萍 《西南民族大学学报(自然科学版)》 CAS 2015年第6期748-753,共6页
首先讨论移动最小二乘插值法,并利用移动最小二乘插值法建立形函数,结合KdV-B方程的Galerkin积分弱形式,提出求KdV-B方程数值解的插值型无单元Galerkin方法(IEFG),并推导其相应的公式,跟无单元Galerkin方法相比,利用插值型无单元Galerki... 首先讨论移动最小二乘插值法,并利用移动最小二乘插值法建立形函数,结合KdV-B方程的Galerkin积分弱形式,提出求KdV-B方程数值解的插值型无单元Galerkin方法(IEFG),并推导其相应的公式,跟无单元Galerkin方法相比,利用插值型无单元Galerkin方法计算时,本质边界条件可直接施加,从而可提高计算效率,并给出算例说明了该方法的有效性. 展开更多
关键词 无网格方法 移动最小二乘插值法 形函数 插值型无单元Galerkin方法(iefg) KDV-B方程
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Solving unsteady Schr?dinger equation using the improved element-free Galerkin method 被引量:3
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作者 程荣军 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第2期35-43,共9页
By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional (2D... By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional (2D) trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square (MLS) approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper. 展开更多
关键词 meshless method improved moving least-square (IMLS) approximation improved element-freeGalerkin iefg method Schr6dinger equation
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The dimension split element-free Galerkin method for three-dimensional potential problems 被引量:4
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作者 Z.J.Meng H.Cheng +1 位作者 L.D.Ma Y.M.Cheng 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第3期462-474,共13页
This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-d... This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method. 展开更多
关键词 Dimension split method Improved moving least-squares (IMLS) approximation Improved element-free Galerkin iefg method Finite difference method (FDM) Dimension split element-free Galerkin (DSEFG) method Potential problem
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The improved element-free Galerkin method forthree-dimensional wave equation 被引量:16
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作者 Zan Zhang Dong-Ming Li +1 位作者 Yu-Min Cheng Kim Moew Liew 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第3期808-818,共11页
The paper presents the improved element-free Galerkin (IEFG) method for three-dimensional wave propa- gation. The improved moving least-squares (IMLS) approx- imation is employed to construct the shape function, w... The paper presents the improved element-free Galerkin (IEFG) method for three-dimensional wave propa- gation. The improved moving least-squares (IMLS) approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares (MLS) approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study. 展开更多
关键词 Weighted orthogonal function Improved mov-ing least squares (IMLS) approximation. Improved element-free Galerkin iefg method Penalty method Temporaldiscretization Wave equation
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Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method 被引量:1
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作者 程荣军 魏麒 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第6期150-155,共6页
In this paper, we analyze the generalized Camassa and Holm (CH) equation by the improved element-free Galerkin (IEFG) method. By employing the improved moving least-square (IMLS) approximation, we derive the for... In this paper, we analyze the generalized Camassa and Holm (CH) equation by the improved element-free Galerkin (IEFG) method. By employing the improved moving least-square (IMLS) approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper. 展开更多
关键词 meshless method improved moving least-square (IMLS) approximation improved element-freeGalerkin iefg method generalized Camassa and Holm (CH) equation
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用插值型无单元Galerkin方法求解广义Fisher方程
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作者 张国达 王迪飞 任红萍 《太原师范学院学报(自然科学版)》 2015年第2期1-7,共7页
首先讨论了移动最小二乘插值法,并利用移动最小二乘插值法建立形函数,结合广义Fisher方程的Galerkin积分弱形式,提出了求广义Fisher方程数值解的插值型无单元Galerkin方法,该方法在求解偏微分方程定解问题时可以直接施加本质边界条件,... 首先讨论了移动最小二乘插值法,并利用移动最小二乘插值法建立形函数,结合广义Fisher方程的Galerkin积分弱形式,提出了求广义Fisher方程数值解的插值型无单元Galerkin方法,该方法在求解偏微分方程定解问题时可以直接施加本质边界条件,这样就提高了求解效率.并给出了数值算例. 展开更多
关键词 无网格方法 移动最小二乘插值法 插值型无单元Galerkin方法 广义FISHER方程
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改进型无网格Galerkin法与有限元法的耦合及其应用研究
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作者 任学军 《安徽建筑工业学院学报(自然科学版)》 2010年第5期8-13,共6页
采用改进型无网格Galerkin法与有限元(IEFG-FE)耦合的方法来计算裂纹问题。改进型无网格伽辽金法是基于一种改进的移动最小二乘(ani mproved moving least-squares,I MLS)近似。I MLS近似比现有的MLS近似有更高的计算效率和精度,且不会... 采用改进型无网格Galerkin法与有限元(IEFG-FE)耦合的方法来计算裂纹问题。改进型无网格伽辽金法是基于一种改进的移动最小二乘(ani mproved moving least-squares,I MLS)近似。I MLS近似比现有的MLS近似有更高的计算效率和精度,且不会导致系统方程产生病态。这种耦合的方法不仅解决了无网格Galerkin法力学边界条件施加的难点,避免系统方程产生病态,而且还克服了无网格Galerkin法耗时较多的缺点。本文运用线弹性断裂力学理论,采用加权正交基函数对有限板单边裂纹的应力强度因子和受拉单边斜裂纹矩形板进行了分析。数值计算结果表明:该方法是一种具有收敛快、精度高、简便有效的通用方法,在工程中具有广阔的应用前景。 展开更多
关键词 IMLS iefg iefg-FE 应力强度因子
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The dimension splitting element-free Galerkin method for 3D transient heat conduction problems 被引量:8
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作者 ZhiJuan Meng Heng Cheng +1 位作者 LiDong Ma YuMin Cheng 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2019年第4期45-56,共12页
By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin(DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin(IE... By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin(DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin(IEFG) method is used for 2D transient heat conduction problems, and the finite difference method is applied in the splitting direction. The discretized system equation is obtained based on the Galerkin weak form of 2D problem; the essential boundary conditions are imposed with the penalty method; and the finite difference method is employed in the time domain. Four exemplary problems are chosen to verify the efficiency of the DSEFG method. The numerical solutions show that the efficiency and precision of the DSEFG method are greater than ones of the IEFG method for 3D problems. 展开更多
关键词 improved element-free GALERKIN (iefg) METHOD DIMENSION SPLITTING METHOD finite DIFFERENCE METHOD DIMENSION SPLITTING element-free GALERKIN (DSEFG) METHOD TRANSIENT heat conduction problem
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