Open Access

ARTICLE

An Accurate Refinement Scheme for Inverse Heat Source Location Identifications

Leevan Ling¹, Tomoya Takeuchi²

1 Department of Mathematics, Hong Kong Baptist Univer-sity, Kowloon Tong, Hong Kong.
2 Graduate School of Mathematical Sciences, University ofTokyo, Tokyo, Japan.

Computer Modeling in Engineering & Sciences 2007, 20(2), 99-110. https://doi.org/10.3970/cmes.2007.020.099

Abstract

We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4):1289--1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence of the proposed algorithm with noisy data is proven. The work is concluded by some numerical examples.

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Keywords

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