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.