导热几何形状反演的变分原理及边界条件的确立  

Variational principle and its boundary and additional boundary conditions for inverse shape design problem of heat conduction

作　　者：吴兆春[1] 

机构地区：[1]上海应用技术学院土木建筑与安全工程系,上海200235

出　　处：《物理学报》2010年第9期6326-6330,共5页Acta Physica Sinica

基　　金：上海应用技术学院科技发展基金(批准号:KJ2009-16)资助的课题~~

摘　　要：本文采用变域变分原理,建立了导热几何形状反演问题的变分原理,同时获得了该问题所需满足的边界条件和附加条件.该变分原理能将未知形状的几何变量及控制方程结合在一个变分泛函中,使得数学描述简洁、紧凑,且几何变量及控制方程的求解能耦合地进行.介绍了运用该变分原理并结合有限元方法进行数值计算的方法.Based on variable domain variational principle （VP）, the variational theory of inverse shape design of heat conduction together with the boundary and the additional boundary conditions enforced on the unknown surface which must be satisfied by the problem is established. Incorporating the boundary and additional conditions into the functional makes the mathematic formulation very concise and compact. Through the established VP,both the temperature field and unknown boundary shape can be determined in a coupled way. The numerical method of the variational principle combined with finite element method is presented in the paper.

关 键 词：几何形状反演 变分原理 有限元 导热 

分 类 号：O411[理学—理论物理]