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

B. Tomas Johansson; Daniel Lesnic; Thomas Reeve

doi:10.1080/00207160.2012.680448

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 journal › Special 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 language	English
Pages (from-to)	1555-1568
Number of pages	14
Journal	International Journal of Computer Mathematics
Volume	89
Issue number	11
Early online date	3 May 2012
DOIs	https://doi.org/10.1080/00207160.2012.680448
Publication status	Published - 2012
Event	8th UK Conference on Boundary Integral Methods - University of Leeds, Leeds, United Kingdom Duration: 4 Jul 2011 → 5 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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10.1080/00207160.2012.680448

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title = "A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems",

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.",

keywords = "heat conduction, method of fundamental solutions, MFS, axisymmetric heat equation, radially symmetric heat equation, backward inverse problem",

author = "Johansson, {B. Tomas} and Daniel Lesnic and Thomas Reeve",

note = "Special Issue: Proceedings of the 8th UK Conference on Boundary Integral Methods, July 4th–5th, 2011, held at the University of Leeds, UK.; 8th UK Conference on Boundary Integral Methods ; Conference date: 04-07-2011 Through 05-07-2011",

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T1 - A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

AU - Johansson, B. Tomas

AU - Lesnic, Daniel

AU - Reeve, Thomas

N1 - Special Issue: Proceedings of the 8th UK Conference on Boundary Integral Methods, July 4th–5th, 2011, held at the University of Leeds, UK.

PY - 2012

Y1 - 2012

N2 - 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.

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.

KW - heat conduction

KW - method of fundamental solutions

KW - MFS

KW - axisymmetric heat equation

KW - radially symmetric heat equation

KW - backward inverse problem

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U2 - 10.1080/00207160.2012.680448

DO - 10.1080/00207160.2012.680448

M3 - Special issue

SN - 0020-7160

VL - 89

SP - 1555

EP - 1568

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 11

T2 - 8th UK Conference on Boundary Integral Methods

Y2 - 4 July 2011 through 5 July 2011

ER -

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

Abstract

Bibliographical note

Keywords

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A method of fundamental solutions for theaxisymmetric backward heat equation

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

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