Simultaneous reconstruction of the surface heat flux and the source term in 3D linear parabolic problem by modified conjugate gradient method. (10th October 2016)

• Record Type: Journal Article
• Authors: Wang, Yuan; Luo, Xiaochuan; Song, Yuqiao; Xie, Qiqi
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 8(2017)
• Page Start: 2847
• Page End: 2858
• Publication Date: 2016-10-10
• Subjects: inverse heat conduction problem -- adjoint approach -- Lipschitz continuity -- improved conjugate gradient method; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4201
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Our work is devoted to an inverse problem for three‐dimensional parabolic partial differential equations. When the surface temperature data are given, the problem of reconstructing the heat flux and the source term is investigated. There are two main contributions of this paper. First, an adjoint problem approach is used for analysis of the Fréchet gradient of the cost functional. Second, an improved conjugate gradient method is proposed to solve this problem. Based on Lipschitz continuity of the gradient, the convergence analysis of the conjugate gradient algorithm is studied. Copyright © 2016 John Wiley & Sons, Ltd.