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

Fingerprint

Method of Fundamental Solutions
Heat Conduction
Heat conduction
Transient Heat Conduction
Temperature Measurement
Ill-posed Problem
Numerical Approximation
Temperature measurement
Heat Equation
Boundary Elements
Computational Cost
Regularization
Generalise
Costs
Temperature

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

Cite this

Johansson, B. Tomas ; Lesnic, Daniel ; Reeve, Thomas. / A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems. In: International Journal of Computer Mathematics. 2012 ; Vol. 89, No. 11. pp. 1555-1568.
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A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems. / Johansson, B. Tomas; Lesnic, Daniel; Reeve, Thomas.

In: International Journal of Computer Mathematics, Vol. 89, No. 11, 2012, p. 1555-1568.

Research output: Contribution to journalSpecial issue

TY - JOUR

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AU - Johansson, B. Tomas

AU - Lesnic, Daniel

AU - Reeve, Thomas

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AB - 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.

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KW - method of fundamental solutions

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