无网格Galerkin方法中权函数的研究  

A study of weight function in element-free Galerkin method

作　　者：杨玉英[1] 李晶[1] 

机构地区：[1]哈尔滨工业大学材料科学与工程学院,哈尔滨150001

出　　处：《塑性工程学报》2005年第4期5-9,共5页Journal of Plasticity Engineering

摘　　要：权函数在无网格Galerkin法(ElementfreeGalerkinMethod,EFGM)中起着非常重要的作用,通过函数中的各个参数控制着对计算精度、计算效率以及收敛速度的影响程度。为详细探讨权函数的作用,分析了常用权函数的曲线特征,得到了影响域半径等各参数对权重大小及分布的影响规律,并在数值算例的基础上进一步研究了它们对计算精度和计算效率的影响,确定出适用于EFGM的权函数。最后,提出弹性误差分析法,实现了对任意形式权函数合理性的判断以及权函数中各参数值的准确确定,并以几种权函数为例,验证了该方法的可行性。Weight function is very important in element-free Galerkin method （EFGM） and its influence to the computational precision, efficiency and convergence rate is controlled by all the parameters in it.To find out the behavior of different weight functions in EFGM in detail, characteristic curves of several weight functions in common use are analyzed and some observations about how the radius of influence domain and other parameters affect the value and distribution of the weight are obtained. Besides, on the basis of a numerical example attributes of these weight functions to computational precision and efficiency are invested and the most applicable weight function to EFGM is settled. Finally, by a new strategy of elastic error analysis the rationality of an arbitrary weight function can be estimated and exact parameter values for the affirmed function are also provided.The feasibility of this analysis method is approved by an example.

关 键 词：无网格GALERKIN法 移动的最小二乘近似 权函数 影响域半径 误差分析 

分 类 号：TB11[理学—数学]