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.
Rashedi, K., Hashemi, A., & Zarhoun, M. (2021). Application of the method of fundamental solutions for designing the optimal shape in heat transfer. Computational Methods for Differential Equations, 9(1), 273-288. doi: 10.22034/cmde.2020.35593.1611
MLA
Kamal Rashedi; Akbar Hashemi; Maryam Zarhoun. "Application of the method of fundamental solutions for designing the optimal shape in heat transfer". Computational Methods for Differential Equations, 9, 1, 2021, 273-288. doi: 10.22034/cmde.2020.35593.1611
HARVARD
Rashedi, K., Hashemi, A., Zarhoun, M. (2021). 'Application of the method of fundamental solutions for designing the optimal shape in heat transfer', Computational Methods for Differential Equations, 9(1), pp. 273-288. doi: 10.22034/cmde.2020.35593.1611
VANCOUVER
Rashedi, K., Hashemi, A., Zarhoun, M. Application of the method of fundamental solutions for designing the optimal shape in heat transfer. Computational Methods for Differential Equations, 2021; 9(1): 273-288. doi: 10.22034/cmde.2020.35593.1611
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