径向基函数在无单元方法中的应用  

Application of radial basis function in meshless method

作　　者：秦伶俐[1] 黄文彬[1] 周喆[1] 

机构地区：[1]中国农业大学理学院,北京100083

出　　处：《中国农业大学学报》2004年第6期80-84,共5页Journal of China Agricultural University

摘　　要：采用基于径向基函数的无单元法求解微分方程 ,探讨 2种径向基函数的性质 ,得到了基函数中自由参数与求解精度的关系曲线 ,以及节点均布时自由参数最佳取值的计算公式及其数值 ;将节点均布下得到的自由参数取值公式应用于节点任意排列的情况 ,其求解精度仍能得到保证 ;比较了无单元方法在节点均布与否 2种情况下的计算精度 ,其求解结果变化不大 ,均满足精度要求 ,说明这种无单元法对节点位置不敏感。The meshless method based on radial basis functions was adopted to solve the differential equations. The properties of the two radial basis functions were investigated and the relational curves of the solution precision and the free parameters in the radial basis functions were obtained. The formula for the optimum value of the free parameter and its calculated value when the nodes were uniformly distributed were also obtained from the solution. We applied that formula to the condition of random nodes and found its solution could still keep a satisfied precision. We compared the computation precisions of the solutions under the conditions of various nodes distributions and the results showed that the precisions didn't change obviously, which meant that this method wasn't sensitive to the distribution of nodes.

关 键 词：径向基函数 无单元法 形函数 δ条件 有限元法 

分 类 号：O241[理学—计算数学]