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

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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.
Language:
English
Published:
Iranian Journal of Numerical Analysis and Optimization, Volume:9 Issue: 1, Winter and Spring 2019
Pages:
1 to 16
https://www.magiran.com/p1950022