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A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
University of Leeds, England .
University of Birmingham, England .
2014 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, Vol. 101, 61-77 p.Article in journal (Refereed) Published
Abstract [en]

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed.

Place, publisher, year, edition, pages
Elsevier , 2014. Vol. 101, 61-77 p.
Keyword [en]
Heat conduction; Inverse Stefan problem; Method of fundamental solutions; Two-phase change; Regularization
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-108156DOI: 10.1016/j.matcom.2014.03.004ISI: 000336693800005OAI: diva2:729652
Available from: 2014-06-26 Created: 2014-06-26 Last updated: 2014-06-26

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Johansson, Tomas
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