Open AccessAn inverse problem in estimating the time dependent source term and initial temperature simultaneously by the polynomial regression and conjugate gradient method
Author(s) -
Arzu Erdem
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2010507c
Subject(s) - tikhonov regularization , mathematics , conjugate gradient method , term (time) , stability (learning theory) , inverse problem , inverse , polynomial , temperature gradient , mathematical optimization , mathematical analysis , computer science , physics , geometry , quantum mechanics , machine learning
From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be effective in dealing with these problems. However, they require to find the gradient information. This idea has been employed in this research. We derive the gradient of Tikhonov functional and establish the stability of the minimizer from the necessary condition. The stability and effectiveness of evolutionary algorithm are presented for various test examples.