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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (4): 623-632.doi: 10.3969/j.issn.1005-3085.2015.04.015

• • 上一篇    

基于共轭方法的热传导问题的间断界面识别(英)

晏文璟1,   段献葆2,   管国兴1   

  1. 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
  • 收稿日期:2014-12-11 接受日期:2015-06-18 出版日期:2015-08-15 发布日期:2015-10-15
  • 基金资助:
    国家自然科学基金 (11371288)；陕西省教育厅研究基金 (11JK0494).

Discontinuity Identification for Heat Conduction Problem Based on the Adjoint Method

YAN Wen-jing1,   DUAN Xian-bao2,   GUAN Guo-xing1   

  1. 1- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
    2- School of Sciences, Xi'an University of Technology, Xi'an 710048
  • Received:2014-12-11 Accepted:2015-06-18 Online:2015-08-15 Published:2015-10-15
  • Supported by:
    The National Natural Science Foundation of China (11371288); the Research Foundation of Department of Education of Shaanxi (11JK0494).

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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．

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

Abstract:

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 results demonstrate the feasibility and effectiveness of the proposed algorithm.

Key words: shape inverse problem, adjoint method, heat conduction, shape gradient, gradient algorithm

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