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On the solution of an inverse natural convection problem using various conjugate gradient methods
Author(s) -
Park H. M.,
Chung O. Y.
Publication year - 2000
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/(sici)1097-0207(20000210)47:4<821::aid-nme799>3.0.co;2-k
Subject(s) - conjugate gradient method , conjugate residual method , natural convection , inverse problem , derivation of the conjugate gradient method , nonlinear conjugate gradient method , inverse , mathematics , gradient method , minification , convection , mathematical analysis , mathematical optimization , mechanics , computer science , gradient descent , physics , geometry , artificial neural network , machine learning
The inverse problem of determining the time‐varying strength of a heat source, which causes natural convection in a two‐dimensional cavity, is considered. The Boussinesq equation is used to model the natural convection induced by the heat source. The inverse natural convection problem is solved through the minimization of a performance function utilizing the conjugate gradient method. The gradient of the performance function needed in the minimization procedure of the conjugate gradient method is obtained by employing either the adjoint variable method or the direct differentiation method. The accuracy and efficiency of these two methods are compared, and a new method is suggested that exploits the advantageous aspects of both methods while avoiding the shortcomings of them. Copyright © 2000 John Wiley & Sons, Ltd.