Inverse shape and surface heat transfer coefficient identification

In this paper, an inverse geometric problem for the modified Helmholtz equation arising in heat conduction in a fin is considered. This problem which consists of determining an unknown inner boundary of an annular domain and possibly its surface heat transfer coefficient from one or two pairs of boundary Cauchy data (boundary temperature and heat flux) is solved numerically using the meshless method of fundamental solutions (MFS). A nonlinear unconstrained minimisation of the objective function is regularised when noise is added to the input boundary data. The stability of the numerical results is investigated for several test examples with respect to noise in the input data and various values of the regularisation parameters.