TY - JOUR T1 - A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem AU - Johansson , B. Tomas AU - Lesnic , Daniel AU - Reeve , Thomas 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, method of fundamental solutions (MFS), inverse Stefan problem, 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.