%0 Journal Article
%T Application of the method of fundamental solutions for designing the optimal shape in heat transfer
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Rashedi, Kamal
%A Hashemi, Akbar
%A Zarhoun, Maryam
%D 2021
%\ 01/01/2021
%V 9
%N 1
%P 273-288
%! Application of the method of fundamental solutions for designing the optimal shape in heat transfer
%K Elliptic equation
%K Optimal shape
%K Method of fundamental solutions
%K Tikhonov regularization
%K Radial basis functions
%R 10.22034/cmde.2020.35593.1611
%X 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 Tikhonovâ€™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.
%U https://cmde.tabrizu.ac.ir/article_10319_3dcd256b467dfd3f322e8f227f965331.pdf