Application of the method of fundamental solutions for designing the optimal shape in heat transfer

In this paper, we propose a meshless regularization technique for solving an optimal shape design problem (OSD) which consists of constructing the optimal configuration of a conducting body subject to given boundary conditions to minimize a certain objective function. This problem also can be seen as the problem of building a support for a membrane such that its deflection is as close as possible to 1 in the subset D of the domain. We propose a numerical technique based on the combination of the method of fundamental solutions and application of the Tikhonov’s regularization method to obtain stable solution. Numerical experiments while solving several test examples are included to show the applicability of the proposed method for obtaining the satisfactory results.