Regularization of the inverse heat conduction problem by the discrete Fourier transform. Issue 2 (12th February 2016)

• Record Type: Journal Article
• Authors: Wróblewska, Agnieszka; Frąckowiak, Andrzej; Ciałkowski, Michał
• Is Part Of: Inverse problems in science and engineering. Volume 24:Issue 2(2016)
• Page Start: 195
• Page End: 212
• Publication Date: 2016-02-12
• Subjects: heat transfer -- inverse problem -- svd algorithm -- Tikhonov regularization -- Fourier transform; 74G75 Inverse problems -- 65F22 Ill-posedness, regularization -- 65T50 Discrete and fast Fourier transforms; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2015.1017480
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : Two methods of solving the inverse heat conduction problem with employment of the discrete Fournier transform are presented in this article. The first one operates similarly to the SVD algorithm and consists in reducing the number of components of the discrete Fournier transform which are taken into account to determine the solution to the inverse problem. The second method is related to the regularization of the solution to the inverse problem in the discrete Fournier transform domain. Those methods were illustrated by numerical examples. In the first example, an influence of the boundary conditions disturbance by a random error on the solution to the inverse problem (its stability) was examined. In the second example, the temperature distribution on the inner boundary of the multiply connected domain was determined. Results of calculations made in both ways brought very good outcomes and confirm the usefulness of applying the discrete Fournier transform to solving inverse problems.