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The boundary-element method for the determination of a heat source dependent on one variable

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Abstract

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions of the direct problem and a supplementary condition, called an overdetermination. In this problem, if the heat source is taken to be space-dependent only, then the overdetermination is the temperature measurement at a given single instant, whilst if the heat source is time-dependent only, then the overdetermination is the transient temperature measurement recorded by a single thermocouple installed in the interior of the heat conductor. These measurements ensure that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method with the discrepancy principle or the L-curve criterion for the choice of the regularization parameter. The boundary-element method (BEM) is developed for solving numerically the inverse problem and numerical results for some benchmark test examples are obtained and discussed

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Authors and Affiliations

  1. BP Institute, University of Cambridge, Cambridge, CB3 0EZ, UK

    Adrian Farcas

  2. Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    Daniel Lesnic

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  1. Adrian Farcas
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  2. Daniel Lesnic
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Correspondence to Adrian Farcas.

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Farcas, A., Lesnic, D. The boundary-element method for the determination of a heat source dependent on one variable. J Eng Math 54, 375–388 (2006). https://doi.org/10.1007/s10665-005-9023-0

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  • DOI: https://doi.org/10.1007/s10665-005-9023-0

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