![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
Abstract
This article presents a computational analysis of the Conjugate Gradient Method (CGM), and a comparative analysis of the method (CGM) and coarse-fine grid algorithm (CFGA) for parabolic inverse coefficient problems (ICPs) based on boundary measured data. The adjoint problem approach is applied to obtain formal gradients of each ICPs as the L2-scalar product of the derivatives ux(x, t; k) and ϕx(x, t; k) of the corresponding direct and adjoint problems. Then the CGM is applied to the least-squares formulation of the inverse coefficient problems. Detailed numerical study of the method for each ICP is presented for various types of type input data concentrated at the boundary. Comparative computational analysis of the CGM and CFGA shows the limits of applications and effectiveness of each these methods.
Acknowledgements
This research has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) through the project No. 108T332. The work of Alemdar Hasanov has also been supported by the International Research Program of L.N. Gumilev Eurasian National University, Astana, Kazakhstan. The authors thank the referees whose comments and suggestions substantially improved the revision of this article.