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A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem

Published online by Cambridge University Press:  03 June 2015

B. Tomas Johansson ,
Daniel Lesnic  and
Thomas Reeve
B. Tomas Johansson*
Affiliation:
Department of Science and Technology, Campus Norrköping, Linköping University, Sweden
Daniel Lesnic*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Thomas Reeve*
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
*
Corresponding author. Email: tomas.johansson@liu.se
Email: amt5ld@maths.leeds.ac.uk
Email: reevet@maths.bham.ac.uk
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Abstract

In this paper, a meshless regularization method of fundamental solutions is proposed for a two-dimensional, two-phase linear inverse Stefan problem. The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions. Furthermore, the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution. Therefore, regularization is necessary in order to obtain a stable solution. Numerical results for several benchmark test examples are presented and discussed.

Keywords

35K0535A3565N3580A22Heat conductionmethod of fundamental solutions (MFS)inverse Stefan problemtwo-phase change
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 6 , December 2013 , pp. 825 - 845
Copyright
Copyright © Global-Science Press 2013

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