Transformation to a fixed domain in LP modelling for a class of optimal shape design problems

Iranian Journal of Numerical Analysis and Optimization

مقاله 1، دوره 9، شماره 1 - شماره پیاپی 15، 2019، صفحه 1-16   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v9i1.53910

نویسندگان

H.H. Mehne^{* 1}؛ M. H. Farahi²

¹Aerospace Research Institute, Tehran,

²Ferdowsi University of Mashhad, Mashhad, Iran.

چکیده

A class of optimal shape design problems is studied in this paper. The boundary shape of a domain is determined such that the solution of the underlying partial differential equation matches, as well as possible, a given desired state. In the original optimal shape design problem, the variable domain is parameterized by a class of functions in such a way that the optimal design problem is changed to an optimal control problem on a fixed domain. Then, the resulting distributed control problem is embedded in a measure theoretical form, in fact, an infinite-dimensional linear programming problem. The optimal measure representing the optimal shape is approximated by a solution of a finite-dimensional linear programming problem. The method is evaluated via a numerical example.

کلیدواژه‌ها

Approximation؛ optimal shape design؛ Linear programming؛ measure theory

مراجع