共查询到20条相似文献,搜索用时 15 毫秒
1.
A meshless Galerkin method with moving least square approximations for infinite elastic solids 下载免费PDF全文
Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method (GBNM), for twoand three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples. 相似文献
2.
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
3.
<正>In this paper,based on the improved complex variable moving least-square(ICVMLS) approximation,a new complex variable meshless method(CVMM) for two-dimensional(2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations,and the essential boundary conditions are imposed by the penalty method.As the transient heat conduction problems are related to time,the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization.Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained.In order to demonstrate the applicability of the proposed method,numerical examples are given to show the high convergence rate,good accuracy,and high efficiency of the CVMM presented in this paper. 相似文献
4.
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
5.
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
6.
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
7.
在移动最小二乘法的基础上,提出了复变量移动最小二乘法.复变量移动最小二乘法的优点是采用一维基函数建立二维问题的逼近函数,所形成的无网格方法计算量小.然后,将复变量移动最小二乘法应用于弹性力学的无网格方法,提出了复变量无网格方法,推导了复变量无网格方法的公式.与传统的无网格方法相比,复变量无网格方法具有计算量小、精度高的优点.最后给出了数值算例.
关键词:
移动最小二乘法
复变量移动最小二乘法
无网格方法
弹性力学
复变量无网格方法 相似文献
8.
A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation 下载免费PDF全文
Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail. 相似文献
9.
A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation 下载免费PDF全文
An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete algebraic equations are established and are solved by an iterative algorithm. Convergence of the iterative algorithm is discussed. Shifted and scaled basis functions are incorporated into the method to guarantee convergence and stability of numerical results. Numerical examples are presented to demonstrate the high convergence rate and high computational accuracy of the method. 相似文献
10.
Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems 下载免费PDF全文
We first give a stabilized improved moving least squares(IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis. 相似文献
11.
This paper presents a meshless method for the nonlinear generalized regularized long wave(GRLW) equation based on the moving least-squares approximation.The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method.A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm.Compared with numerical methods based on mesh,the meshless method for the GRLW equation only requires the scattered nodes instead of meshing the domain of the problem.Some examples,such as the propagation of single soliton and the interaction of two solitary waves,are given to show the effectiveness of the meshless method. 相似文献
12.
将滑动Kriging插值法与无网格局部Petrov-Galerkin法相结合,采用Heaviside分段函数作为局部弱形式的权函数,提出改进的无网格局部Petrov-Galerkin法,进一步将这种无网格法应用于位势问题,并推导相应的离散方程.因为滑动Kriging插值法构造的形函数满足Kronecker函数性质,所以本文建立的改进的无网格局部Petrov-Galerkin法可以像有限元法一样直接施加边界条件;由于采用Heaviside分段函数作为局部弱形式的权函数,因此在计算刚度矩阵时只涉及边界积分,而没有区域积分.此外,还对本方法中一些重要参数的选取进行了研究.数值算例表明,本文建立的改进的无网格局部Petrov-Galerkin法具有数值实现简单、计算量小以及方便施加边界条件等优点. 相似文献
13.
针对现有的相位提取算法只对某些特定的误差不敏感,不能满足高精度光学检测的要求,本文引入一种等间隔多步移相算法—权重待定的加权最小二乘算法。通过在最小二乘算法中添加待定的权重,分析移相点衍射干涉仪中多种误差源对算法的影响,获得多组约束方程,从而确定权重和新算法。对新算法和标准四步算法、Hariharan五步算法进行比对分析,验证了新算法对PZT线性和二阶非线性移相不准、光强的一阶二阶波动和光源频率一阶二阶波动等误差抑制能力远远优于标准四步算法和Hariharan五步算法;新算法对CCD的量化误差、光强噪声、频率噪声的抑制能力也具有一定优势,且对CCD的二阶响应非线性完全不敏感。 相似文献
14.
This paper presents a new compact approximation method for the discretisation of second-order elliptic equations in one and two dimensions. The problem domain, which can be rectangular or non-rectangular, is represented by a Cartesian grid. On stencils, which are three nodal points for one-dimensional problems and nine nodal points for two-dimensional problems, the approximations for the field variable and its derivatives are constructed using integrated radial basis functions (IRBFs). Several pieces of information about the governing differential equation on the stencil are incorporated into the IRBF approximations by means of the constants of integration. Numerical examples indicate that the proposed technique yields a very high rate of convergence with grid refinement. 相似文献
15.
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
16.
A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction 下载免费PDF全文
A method of modifying the architecture of fractional least mean square (FLMS) algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square (MFLMS) algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts. 相似文献
17.
针对紫外光通信中传统自适应最小均方(LMS)算法存在的不足,提出了一种新的变步长LMS(VSS-LMS)算法,利用MATLAB仿真验证了该算法的可行性,以TMS320VC5509为核心设计了数字信号处理(DSP)最小化硬件系统和VSS-LMS算法的软件流程,在硬件上实现了传统LMS算法和新的VSS-LMS算法的自适应滤波,并进行了对比分析,结果表明所提出的VSS-LMS算法具有较快的收敛速度和较小的稳态误差,这对紫外光通信接收系统的设计和优化具有一定的参考意义。 相似文献
18.
19.
A moving Kriging interpolation-based boundary node method for two-dimensional potential problems 下载免费PDF全文
In this paper,a meshfree boundary integral equation(BIE) method,called the moving Kriging interpolationbased boundary node method(MKIBNM),is developed for solving two-dimensional potential problems.This study combines the BIE method with the moving Kriging interpolation to present a boundary-type meshfree method,and the corresponding formulae of the MKIBNM are derived.In the present method,the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker’s delta property,then the boundary conditions can be imposed directly and easily.To verify the accuracy and stability of the present formulation,three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically. 相似文献
20.
An improved boundary element-free method (IBEFM) for two-dimensional potential problems 总被引:1,自引:0,他引:1 下载免费PDF全文
The interpolating moving least-squares (IMLS) method is discussed
first in this paper. And the formulae of the IMLS method obtained by
Lancaster are revised. Then on the basis of the boundary
element-free method (BEFM), combining the boundary integral equation
(BIE) method with the IMLS method, the improved boundary
element-free method (IBEFM) for two-dimensional potential problems
is presented, and the corresponding formulae of the IBEFM are
obtained. In the BEFM, boundary conditions are applied directly, but
the shape function in the MLS does not satisfy the property of
the Kronecker δ function. This is a problem of the BEFM, and
must be solved theoretically. In the IMLS method, when the shape function
satisfies the property of the Kronecker δ function, then the
boundary conditions, in the meshless method based on the IMLS
method, can be applied directly. Then the IBEFM, based on the IMLS
method, is a direct meshless boundary integral equation method in
which the basic unknown quantity is the real solution of the nodal
variables, and the boundary conditions can be applied directly and
easily, thus it gives a greater computational precision. Some
numerical examples are presented to demonstrate the method. 相似文献