广义边界控制法在多层热传导边界识别问题中的应用  

A General Boundary Control Method Based on FEM for Boundary Identification in a Multi-Layer Heat Conduction

作　　者：岳俊宏 李明[1] 牛瑞萍[1] 

机构地区：[1]太原理工大学数学学院,太原030024

出　　处：《太原理工大学学报》2016年第4期545-551,共7页Journal of Taiyuan University of Technology

基　　金：国家自然科学基金资助项目:可商业化光滑有限元分析软件的研发(11472184);国家青年科学基金资助项目:牙种植技术中的多参数识别问题的计算方法(11401423)

摘　　要：基于有限元(FEM)的广义边界控制法可应用于求解固体力学的反问题。带有柯西数据(部分边界的温度值与热流值)的多层热传导边界识别问题是一类反向热传导问题。研究用该方法求解带有柯西数据的一维多层热传导边界识别问题,并证明了该方法的可行性。数值实例证实基于有限元的广义边界控制法对多层热传导边界识别问题是有效且稳定的。The general boundary control method （GBCM） based on finite element method （FEM） has been applied to solve inverse solid mechanics problems. The identification of a moving boundary for multi-layer heat conduction with Cauchy boundary data is a typical inverse heat con- duction problem. In this paper, the boundary identification problem of one-dimensional multi-lay- er heat conduction is solved using the GBCM based on FEM. Meanwhile, the feasibility of this method is proved. Numerical experiments are presented to demonstrate that the method is effec- tive and stable.

关 键 词：有限元 广义边界控制法 多层热传导 边界识别 

分 类 号：O241[理学—计算数学]