A method of fundamental solutions for theaxisymmetric backward heat equation

B. Tomas Johansson; Daniel Lesnic; Thomas Reeve

A method of fundamental solutions for theaxisymmetric backward heat equation

B. Tomas Johansson, Daniel Lesnic, Thomas Reeve

Mathematics

Research output: Chapter in Book/Published conference output › Conference publication

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
Title of host publication	Advances in boundary integral methods: proceedings of the Eight UK Conference on Boundary Integral Methods
Pages	9-16
Number of pages	7
Publication status	Published - 2011
Event	8th UK Conference on Boundary Integral Methods - University of Leeds, Leeds, United Kingdom Duration: 4 Jul 2011 → 5 Jul 2011

Conference

Conference	8th UK Conference on Boundary Integral Methods
Country/Territory	United Kingdom
City	Leeds
Period	4/07/11 → 5/07/11

1 Conference publication
1 Special issue

A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems
Johansson, B. T., Lesnic, D. & Reeve, T., 2012, In: International Journal of Computer Mathematics. 89, 11, p. 1555-1568 14 p.
Research output: Contribution to journal › Special issue
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/Published conference output › Conference publication

Cite this

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title = "A method of fundamental solutions for theaxisymmetric backward heat equation",

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.",

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

year = "2011",

language = "English",

pages = "9--16",

booktitle = "Advances in boundary integral methods: proceedings of the Eight UK Conference on Boundary Integral Methods",

note = "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 theaxisymmetric backward heat equation

AU - Johansson, B. Tomas

AU - Lesnic, Daniel

AU - Reeve, Thomas

PY - 2011

Y1 - 2011

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.

M3 - Conference publication

SP - 9

EP - 16

BT - Advances in boundary integral methods: proceedings of the Eight UK Conference on Boundary Integral Methods

T2 - 8th UK Conference on Boundary Integral Methods

Y2 - 4 July 2011 through 5 July 2011

ER -

A method of fundamental solutions for theaxisymmetric backward heat equation

Abstract

Conference

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Research output

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

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

Cite this