Open AccessHeat Source Estimation with the Conjugate Gradient Method in Inverse Linear Diffusive Problems
Author(s) -
Jian Su,
Antônio José da Silva Neto
Publication year - 2001
Publication title -
revista brasileira de ciências mecânicas
Language(s) - English
Resource type - Journals
ISSN - 0100-7386
DOI - 10.1590/s0100-73862001000300005
Subject(s) - conjugate gradient method , inverse problem , thermal conduction , derivation of the conjugate gradient method , mathematics , conjugate residual method , nonlinear conjugate gradient method , inverse , work (physics) , heat transfer , heat equation , mathematical analysis , mathematical optimization , gradient descent , computer science , physics , mechanics , geometry , thermodynamics , artificial neural network , machine learning
In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates