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Numerical Methods for Inverse Problem of Heat Conduction with Unknown Boundary Based on Variational Principles with Variable Domain
作者姓名:LiuGao-Lian  ZhangDao-Fang
作者单位:Liu Gao-Lian Shanghai University of Technology and Shanghai Institute of Appl.Math.& Mechanics Shanghai 200072,China Zhang Dao-Fang Shanghai Institute of Mechanical Engineering,Shanghai 200093,China Professor Research Assistant
摘    要:In this article a variable-domain variational approach to the entitled problem is presented.A pair of comple-mentary variational principles with a variable domain in terms of temperature and heat-streamfunction are firstestablished.Based on them,two methods of solution—generalized Ritz method and variable-domain FEM—both capable of handling problems with unknown boundaries,are suggested.Then,three sample numericalexamples have been tested.The computational process is quite stable,and the results are encouraging.Thisvariational approach can be extended straightforwardly to 3-D inverse problems as well as to other problems inmathematical physics.

关 键 词:热传导  反演问题  变分原理
收稿时间:15 August 1992

Numerical methods for inverse problem of heat conduction with unknown boundary based on variational principles with variable domain
Gao-Lian Liu,Dao-Fang Zhang.Numerical Methods for Inverse Problem of Heat Conduction with Unknown Boundary Based on Variational Principles with Variable Domain[J].Journal of Thermal Science,1992,1(4):241-248.
Authors:Gao-Lian Liu  Dao-Fang Zhang
Affiliation:(1) Shanghai University of Technology and Shanghai Institute of Appl. Math. & Mechanics, 200072 Shanghai, China;(2) Shanghai Institute of Mechanical Engineering, 200093 Shanghai, China
Abstract:In this article a variable-domain variational approach to the entitled problem is presented. A pair of complementary variational principles with a variable domain in terms of temperature and heat-streamfunction are first established. Based on them, two methods of solution—generalized Ritz method and variable-domain FEM—both capable of handling problems with unknown boundaries, are suggested. Then, three sample numerical examples have been tested. The computational process is quite stable, and the results are encouraging. This variational approach can be extended straightforwardly to 3-D inverse problems as well as to other problems in mathematical physics.
Keywords:variable-domain variational method  inverse heat conduction problem  unknown boundary  generalized Ritz method  finite element method
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