University of TabrizComputational Methods for Differential Equations2345-39829120210101Application of the method of fundamental solutions for designing the optimal shape in heat transfer2732881031910.22034/cmde.2020.35593.1611ENKamalRashediDepartment of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran0000-0001-7826-1954AkbarHashemiDepartment of Mathematics,
University of Science and Technology of Mazandaran, Behshahr, IranMaryamZarhounDepartment of Mathematics,
University of Science and Technology of Mazandaran, Behshahr, IranJournal Article20190913In 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.https://cmde.tabrizu.ac.ir/article_10319_3dcd256b467dfd3f322e8f227f965331.pdf