A Gaussian RBFs method with regularization for the numerical solution of inverse heat conduction problems. Issue 9 (21st November 2016)

• Record Type: Journal Article
• Authors: Zhang, Yong-Fu; Li, Chong-Jun
• Is Part Of: Inverse problems in science and engineering. Volume 24:Issue 9(2016)
• Page Start: 1606
• Page End: 1646
• Publication Date: 2016-11-21
• Subjects: Inverse heat conduction problem -- numerical recursion scheme -- time-dependent heat source -- radial basis functions -- Neumann boundary conditions -- regularization methods; 65M32 -- 65F22 -- 65D05; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2015.1131825
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : In this paper, a recursion numerical technique is considered to solve the inverse heat conduction problems, with an unknown time-dependent heat source and the Neumann boundary conditions. The numerical solutions of the heat diffusion equations are constructed using the Gaussian radial basis functions. The details of algorithms in the one-dimensional and two-dimensional cases, involving the global or partial initial conditions, are proposed, respectively. The Tikhonov regularization method, with the generalized cross-validation criterion, is used to obtain more stable numerical results, since the linear systems are badly ill-conditioned. Moreover, we propose some results of the condition number estimates to a class of positive define matrices constructed by the Gaussian radial basis functions. Some numerical experiments are given to show that the presented schemes are favourably accurate and effective.