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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  • Research Output

    • 2 Conference publication

    A method of fundamental solutions for theaxisymmetric backward heat equation

    Johansson, B. T., Lesnic, D. & Reeve, T., 2011, Advances in boundary integral methods: proceedings of the Eight UK Conference on Boundary Integral Methods. p. 9-16 7 p.

    Research output: Chapter in Book/Report/Conference proceedingConference publication

  • On a boundary integral equation method for numerical construction of harmonic functions in three-dimensional multilayer domains with a bounded inclusion

    Johansson, T. B., Chapko, R. S., Protsyuk, O. B. & Lesnic, D., 2011, Advances in boundary integral methods: proceedings of the Eight UK Conference on Boundary Integral Methods. p. 88-94 7 p.

    Research output: Chapter in Book/Report/Conference proceedingConference publication

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