Volume 5, Issue 6
A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem

B. Tomas Johansson, Daniel Lesnic & Thomas Reeve

Adv. Appl. Math. Mech., 5 (2013), pp. 825-845.

Published online: 2013-05

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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

Heat conduction method of fundamental solutions (MFS) inverse Stefan problem two-phase change

  • AMS Subject Headings

35K05 35A35 65N35 80A22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-825, author = {B. Tomas Johansson, Daniel Lesnic and Thomas Reeve}, title = {A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {6}, pages = {825--845}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m77}, url = {http://global-sci.org/intro/article_detail/aamm/98.html} }
TY - JOUR T1 - A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem AU - B. Tomas Johansson, Daniel Lesnic & Thomas Reeve JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 825 EP - 845 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.2013.m77 UR - https://global-sci.org/intro/article_detail/aamm/98.html KW - Heat conduction KW - method of fundamental solutions (MFS) KW - inverse Stefan problem KW - two-phase change AB -

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.

B. Tomas Johansson, Daniel Lesnic & Thomas Reeve. (1970). A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem. Advances in Applied Mathematics and Mechanics. 5 (6). 825-845. doi:10.4208/aamm.2013.m77
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