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

Document Type : Research Article

Authors

• H.H. Mehne ¹
• M. H. Farahi ²

¹ Aerospace Research Institute, Tehran,

² Ferdowsi University of Mashhad, Mashhad, Iran.

10.22067/ijnao.v9i1.53910

Abstract

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.

Keywords

• Approximation
• optimal shape design
• Linear programming
• measure theory

20.1001.1.24236977.2019.9.1.1.4

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References

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