A smoothing spline-based regularization of the initial inverse problem in a two-dimensional heat equation

K. Masood; M. Mustafa

doi:10.1243/09544062JMES1123

A smoothing spline-based regularization of the initial inverse problem in a two-dimensional heat equation

K. Masood^*, M. Mustafa

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A smoothing spline-based method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model in two-dimensions. An ill-posed inverse problem involving recovery of the initial temperature distribution from measurements of the final temperature distribution is investigated. A hyperbolic heat conduction model is considered instead of a parabolic model and smoothing splines are applied to regularize the recovered initial profile. The comparison of the proposed procedure and parabolic model is presented graphically by examples.

Original language	English
Pages (from-to)	439-449
Number of pages	11
Journal	Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Volume	223
Issue number	2
DOIs	https://doi.org/10.1243/09544062JMES1123
State	Published - Feb 2009

Keywords

Heat equation
Inverse problem
Regularization
Smoothing splines

ASJC Scopus subject areas

Mechanical Engineering

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10.1243/09544062JMES1123

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abstract = "A smoothing spline-based method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model in two-dimensions. An ill-posed inverse problem involving recovery of the initial temperature distribution from measurements of the final temperature distribution is investigated. A hyperbolic heat conduction model is considered instead of a parabolic model and smoothing splines are applied to regularize the recovered initial profile. The comparison of the proposed procedure and parabolic model is presented graphically by examples.",

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N2 - A smoothing spline-based method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model in two-dimensions. An ill-posed inverse problem involving recovery of the initial temperature distribution from measurements of the final temperature distribution is investigated. A hyperbolic heat conduction model is considered instead of a parabolic model and smoothing splines are applied to regularize the recovered initial profile. The comparison of the proposed procedure and parabolic model is presented graphically by examples.

AB - A smoothing spline-based method and a hyperbolic heat conduction model is applied to regularize the recovery of the initial profile from a parabolic heat conduction model in two-dimensions. An ill-posed inverse problem involving recovery of the initial temperature distribution from measurements of the final temperature distribution is investigated. A hyperbolic heat conduction model is considered instead of a parabolic model and smoothing splines are applied to regularize the recovered initial profile. The comparison of the proposed procedure and parabolic model is presented graphically by examples.

KW - Heat equation

KW - Inverse problem

KW - Regularization

KW - Smoothing splines

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DO - 10.1243/09544062JMES1123

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ER -

A smoothing spline-based regularization of the initial inverse problem in a two-dimensional heat equation

Abstract

Keywords

ASJC Scopus subject areas

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