基于共轭方法的热传导问题的间断界面识别（英文）  

Discontinuity Identification for Heat Conduction Problem Based on the Adjoint Method

作　　者：晏文璟[1] 段献葆[2] 管国兴[1] 

机构地区：[1]西安交通大学数学与统计学院,西安710049 [2]西安理工大学理学院,西安710048

出　　处：《工程数学学报》2015年第4期623-632,共10页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11371288);the Research Foundation of Department of Education of Shaanxi(11JK0494)

摘　　要：本文研究了热传导方程的间断界面形状识别问题.首先,我们基于连续共轭方法,利用函数空间参数化方法和鞍点可微性定理,推导出目标函数的形状梯度.然后构造出求解该形状反问题的梯度型算法.最终,数值模拟的结果验证了所用方法的有效性和可行性.In this paper, we consider the shape inverse problem of discontinuity identification for the heat conduction. Based on the continuous adjoint method, we derive the structure of the derivative for the cost functional by employing the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. Moreover, we present a gradient-type algorithm to the shape inverse problem. Finally, numerical effectiveness of the proposed algorithm. results demonstrate the feasibility and

关 键 词：形状反问题 共轭方法 热传导方程 形状梯度 梯度算法 

分 类 号：O241.82[理学—计算数学]