热传导问题杂交基本解有限元法虚拟源点的探究  

Research on the Fictitious Source Points of the Hybrid Fundamental Solution-Based Finite Element Method for Heat Conduction Problems

作　　者：张凯 王克用 齐东平 ZHANG Kai;WANG Keyong;QI Dongping(School of Mechanical and Automotive Engineering,Shanghai University of Engineering Science,Shanghai 201620,P.R.China)

机构地区：[1]上海工程技术大学机械与汽车工程学院,上海201620

出　　处：《应用数学和力学》2023年第4期431-440,共10页Applied Mathematics and Mechanics

基　　金：上海市自然科学基金项目(19ZR1421400)。

摘　　要：针对热传导问题,提出了杂交基本解有限元法.首先,假设两个独立场:一个为利用基本解线性组合近似的单元域内温度场,另一个为使用与传统有限元法相同形式的辅助网线温度场.然后,利用修正变分泛函将上述两个独立场关联起来,并导出有限元列式.然而,该方法的准确性很大程度上取决于源点的分布和数量,通常将源点布置在单元外部两种虚拟边界上:与单元相似的边界和圆形边界.此外,还提出了双重虚拟边界,并与上述两种源点布局方式进行对比.通过两个典型数值算例,验证了该文方法在不同源点布局下的有效性和对网格畸变的不敏感性.The hybrid fundamental solution-based finite element method was proposed for heat conduction problems.Firstly,2 independent fields were assumed:the intra-element temperature field approximated through the linear combination of fundamental solutions,and the auxiliary frame temperature field in the same form as that in the conventional finite element method.Then,a modified variational functional was employed to link the 2 independent fields and derive the finite element formulation.However,the accuracy of the method is strongly dependent on the distribution and the number of source points.The source points were usually placed on 2 fictitious boundaries outside the element:one is similar to the element shape,the other is a circular one.Furthermore,the dual fictitious boundary scheme was proposed for comparison with the above fictitious boundaries.With different configurations of source points,2 typical numerical examples were given to demonstrate the validity and the insensitivity to mesh distortion of the proposed method.

关 键 词：基本解 有限元法 修正变分泛函 虚拟边界 网格畸变 

分 类 号：O242.21[理学—计算数学] O343.1[理学—数学]