An accurate refinement scheme for inverse heat source location identifications

Leevan Ling; Tomoya Takeuchi

An accurate refinement scheme for inverse heat source location identifications

Leevan Ling^*, Tomoya Takeuchi

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

2 Citations (Scopus)

Abstract

We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4): 1289-1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence of the proposed algorithm with noisy data is proven. The work is concluded by some numerical examples.

Original language	English
Pages (from-to)	99-110
Number of pages	12
Journal	CMES - Computer Modeling in Engineering and Sciences
Volume	20
Issue number	2
Publication status	Published - Jun 2007

Scopus Subject Areas

Software
Modelling and Simulation
Computer Science Applications

User-Defined Keywords

Heat equation
inverse problem
point source
locations identification
fundamental solution
convergence

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https://www.techscience.com/CMES/v20n2/25023

Cite this

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title = "An accurate refinement scheme for inverse heat source location identifications",

abstract = "We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4): 1289-1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence of the proposed algorithm with noisy data is proven. The work is concluded by some numerical examples.",

keywords = "Heat equation, inverse problem, point source, locations identification, fundamental solution, convergence",

author = "Leevan Ling and Tomoya Takeuchi",

note = "This work was supported by the FRG Grants (FRG/06-07/II-30) of Hong Kong Baptist University. The second named author was supported partially by the 21 century COE program at the Graduate School of Mathematical Sciences of the University of Tokyo.",

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month = jun,

language = "English",

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T1 - An accurate refinement scheme for inverse heat source location identifications

AU - Ling, Leevan

AU - Takeuchi, Tomoya

N1 - This work was supported by the FRG Grants (FRG/06-07/II-30) of Hong Kong Baptist University. The second named author was supported partially by the 21 century COE program at the Graduate School of Mathematical Sciences of the University of Tokyo.

PY - 2007/6

Y1 - 2007/6

N2 - We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4): 1289-1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence of the proposed algorithm with noisy data is proven. The work is concluded by some numerical examples.

AB - We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4): 1289-1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence of the proposed algorithm with noisy data is proven. The work is concluded by some numerical examples.

KW - Heat equation

KW - inverse problem

KW - point source

KW - locations identification

KW - fundamental solution

KW - convergence

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M3 - Journal article

AN - SCOPUS:34547817117

SN - 1526-1492

VL - 20

SP - 99

EP - 110

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

IS - 2

ER -

An accurate refinement scheme for inverse heat source location identifications

Abstract

Scopus Subject Areas

User-Defined Keywords

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