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The identification of a Robin coefficient by a conjugate gradient method
Author(s) -
Yang Fenglian,
Yan Liang,
Wei Ting
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2507
Subject(s) - conjugate gradient method , convergence (economics) , conjugate residual method , inverse problem , mathematics , boundary (topology) , derivation of the conjugate gradient method , gradient method , nonlinear conjugate gradient method , additive schwarz method , grid , mathematical optimization , mathematical analysis , computer science , gradient descent , finite element method , domain decomposition methods , geometry , artificial neural network , physics , machine learning , economics , thermodynamics , economic growth
This paper investigates a non‐linear inverse problem associated with the heat conduction problem of identifying a Robin coefficient from boundary temperature measurement. The variational formulation of the problem is given. The conjugate gradient method combining with the discrepancy principle for choosing the suitable stop step are proposed for solving the optimization problem, in which the finite difference method is used to solve the direct problems. The performance of the method is verified by simulating four examples. The convergence with respect to the grid refinement and the amount of noise in the data is also investigated. Copyright © 2008 John Wiley & Sons, Ltd.