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A computational method for identifying a spacewise‐dependent heat source
Author(s) -
Yan Liang,
Fu ChuLi,
Dou FangFang
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1155
Subject(s) - singular value decomposition , heat equation , regularization (linguistics) , mathematics , inverse problem , matrix (chemical analysis) , finite difference method , finite difference scheme , finite difference , singular value , mathematical analysis , mathematical optimization , computer science , algorithm , physics , eigenvalues and eigenvectors , materials science , quantum mechanics , artificial intelligence , composite material
In this paper, we consider a finite difference approximation to an inverse problem of determining a spacewise‐dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time. Since the resulting matrix equation is ill‐conditioned, a regularized solution is obtained by employing the truncated singular value decomposition to solve the matrix equation arising from the finite difference method, with the optimal regularization parameter determined by the generalized cross‐validation criterion. The effectiveness of the proposed numerical scheme is illustrated by several continuous and discontinuous numerical examples. Copyright © 2008 John Wiley & Sons, Ltd.