A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

B. Tomas Johansson, Daniel Lesnic, Thomas Reeve

    Research output: Contribution to journalSpecial issue

    Abstract

    We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.
    Original languageEnglish
    Pages (from-to)1555-1568
    Number of pages14
    JournalInternational Journal of Computer Mathematics
    Volume89
    Issue number11
    Early online date3 May 2012
    DOIs
    Publication statusPublished - 2012
    Event8th UK Conference on Boundary Integral Methods - University of Leeds, Leeds, United Kingdom
    Duration: 4 Jul 20115 Jul 2011

    Bibliographical note

    Special Issue: Proceedings of the 8th UK Conference on Boundary Integral Methods, July 4th–5th, 2011, held at the University of Leeds, UK.

    Keywords

    • heat conduction
    • method of fundamental solutions
    • MFS
    • axisymmetric heat equation
    • radially symmetric heat equation
    • backward inverse problem

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