共查询到19条相似文献,搜索用时 656 毫秒
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一个简洁的最小二乘法拟合程序陈乃强(河北师范学院物理系石家庄050091)用最小二乘法对含有随机误差的离散数据进行曲线拟合,能将变量x与y间变化关系的m对测量值,总结成x、y间最可几的函数表达式y=f(x).但由于此方法所需计算量甚大,故只有在微机已... 相似文献
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主要论述基扩充的无网格法(MLM)用于2D电磁问题计算时的具体算法及编程问题。以独特的分步骤操作方法,介绍了无网格方法;从数值拟合的角度,对无网格伽辽金法(EFG)的核心技术——移动最小二乘法进行了深入剖析;严格按照加权余量法原理,利用偏微分方程的余量加权在节点支持域上的积分,导出了基扩充的EFG离散格式;应用FEM和基扩充的EFG两种方法对一些实例进行了计算验证。 相似文献
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基于移动最小二乘法在Sobolev空间Wk,p(Ω)中的误差估计以及弹性力学问题的变分弱形式中出现的双线性形式的连续性和强制性,研究了弹性力学问题的无单元Galerkin方法的误差分析以及数值解的误差和影响域半径之间的关系,给出了弹性力学问题的无单元Galerkin方法在Sobolev空间中的误差估计定理,并证明了当节点和形函数满足一定条件时该误差估计是最优阶的.从误差分析中可以看出,数值解的误差与权函数的影响域半径密切相关.最后,通过算例验证了结论的正确性.
关键词:
无网格方法
无单元Galerkin方法
弹性力学
误差估计 相似文献
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采用具有离散点插值特性的重构核粒子法形函数, 较精确地重构弹性体 变形的位移试函数, 再与弹性力学的最小势能原理相结合, 形成新的分析弹性力 学平面问题的插值型重构核粒子法. 由于插值型重构核粒子法形函数具有点插值特性和不低于核函数 的高阶光滑性, 因而既克服了多数无网格方法处理本质边界条件的困难, 也保证了较高的数值精度. 与早期的无网格方法相比, 本方法具有精度高、解题规模较小、可直接施加边界条件等优点. 通过对典型弹性力学问题数值模拟, 验证了所提方法的有效性和正确性. 相似文献
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A complex variable meshless method for fracture problems 总被引:4,自引:0,他引:4
CHENG Yumin & LI Jiuhong . Shanghai Institute of Applied Mathematics Mechanics Shanghai University Shanghai China . Department of Building Engineering Xi’an University of Technology Xi’an China 《中国科学G辑(英文版)》2006,49(1):46-59
1 Introduction The meshless (or meshfree) method has been a hot topic and the development trend of numerical methods for many science and engineering problems in recent years. Comparing with the conventional numerical methods, such as the finite element method and the boundary element method, the meshless method is an approximation based on nodes, and does not form a mesh to determine the shape function in the domain, in which a problem is to be solved. The meshless method has some advantages … 相似文献
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A new complex variable element-free Galerkin method for two-dimensional potential problems 下载免费PDF全文
In this paper, based on the element-free Galerkin (EFG) method and the improved complex variable moving least- square (ICVMLS) approximation, a new meshless method, which is the improved complex variable element-free Galerkin (ICVEFG) method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square (CVMLS) approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method. 相似文献
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The complex variable meshless local Petrov—Galerkin method of solving two-dimensional potential problems 下载免费PDF全文
Based on the complex variable moving least-square(CVMLS) approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin(CVMLPG) method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square(MLS) approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin(MLPG) method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method. 相似文献
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The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system,
and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed
a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method
has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system.
A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation
method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless
method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are
the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method
has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method
for elastodynamics problems is presented in this paper. Finally, some numerical examples are given. 相似文献
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Boundary element-free method for elastodynamics 总被引:3,自引:0,他引:3
CHENG Yumin & PENG Miaojuan . Shanghai Institute of Applied Mathematics Mechanics Shanghai University Shanghai China . Department of Civil Engineering Shanghai University Shanghai China 《中国科学G辑(英文版)》2005,48(6):641-657
1 Introduction In recent years, more and more attention has been paid to researches on the meshless (or meshfree) method, which makes it a hot direction of computational mechanics[1,2]. The meshless method is the approximation based on nodes, then the large deformation and crack growth problems can be simulated with the method without the re-meshing technique. And the meshless method has some advantages over the traditional computa- tional methods, such as finite element method (FEM) and boun… 相似文献
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A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems 下载免费PDF全文
On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional (2D) problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method (FEM). This comparison illustrates the accuracy as well as the capability of the CVMLPG method. 相似文献
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In this paper,an improved complex variable meshless method(ICVMM) for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square(ICVMLS) approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency. 相似文献
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Based on the complex variable moving least-square (CVMLS) approximation, the complex variable element-free Galerkin (CVEFG) method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper. The Galerkin weak form is employed to obtain the equation system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin (EFG) method, with the same node distribution, the CVEFG method has higher precision, and to obtain the similar precision, the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method. 相似文献
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In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, an improved complex variable meshless method (ICVMM) for two-dimensional advection-diffusion problems is developed. The equivalent functional of two-dimensional advection-diffusion problems is formed, the variation method is used to obtain the equation system, and the penalty method is employed to impose the essential boundary conditions. The difference method for two-point boundary value problems is used to obtain the discrete equations. Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented. Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper. It is shown that the ICVMM is very effective for advection-diffusion problems, and has good convergent character, accuracy, and computational efficiency. 相似文献