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ZHAO Guang-ming 《应用数学和力学(英文版)》2005,26(8):982-988
IntroductionMeshless methods, as a special numerical method, originated from1970s. Since thediffuse element method was proposed by Nayroleset al.[1]in1992, the meshless methodshave received wide attentions in the mechanics area, and have shown obvious adv… 相似文献
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1 引言基于网格的方法(如有限体积法、有限元法等)是目前流动问题数值求解的主流方法.为了描述流动状态的演化过程并保证其计算精度,运用基于网格的数值方法求解流动问题往往需要不断地生成网格,而这种网格的生成通常需要耗费较多的人力和时间.无网格 相似文献
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Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method 下载免费PDF全文
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. 相似文献
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The element-free Galerkin (EFG) method is used in this paper to find the numerical solution to a regularized long-wave (RLW) equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investigated by two numerical examples in this paper. 相似文献
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The improved element-free Galerkin(IEFG) method of elasticity is used to solve the topology optimization problems.In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin(EFG) method. The central processing unit(CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown. 相似文献
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By employing the improved moving least-square (IMLS) approximation, the improved element-free Galerkin (IEFG) method is presented for the unsteady Schrödinger 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. 相似文献
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An improved element-free Galerkin method for solving generalized fifth-order Korteweg-de Vries equation 下载免费PDF全文
In this paper, an improved element-free Galerkin (IEFG) method is proposed to solve the generalized fifth-order Korteweg-de Vries (gfKdV) equation. When the traditional element-free Galerkin (EFG) method is used to solve such an equation, unstable or even wrong numerical solutions may be obtained due to the violation of the consistency conditions of the moving least-squares (MLS) shape functions. To solve this problem, the EFG method is improved by employing the improved moving least-squares (IMLS) approximation based on the shifted polynomial basis functions. The effectiveness of the IEFG method for the gfKdV equation is investigated by using some numerical examples. Meanwhile, the motion of single solitary wave and the interaction of two solitons are simulated using the IEFG method. 相似文献
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基于径向基函数的无单元法求解力学问题误差分析 总被引:1,自引:0,他引:1
径向基函数形状参数的选择在无单元法数值计算中一直是一个热门的问题,现在已总结出许多确定形状参数的经验公式. 但还没有相关研究表明这些形状参数是如何随着影响域尺寸而变化的. 本文研究了MQ(multi-quadrics) 径向基函数中形状参数对无单元法计算误差的影响. 首先,从理论上分析了形函数导数随着形状参数值的变化趋势,和以计算点为中心节点对称布置与不对称布置的形函数导数的变化规律;然后分析了影响域尺寸对误差的影响,得到了在不同影响域尺寸下,误差随形状参数值变化的规律;在此基础上,给出了影响域范围值. 相似文献