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An iterative method for optimal control of bilateral free boundaries problem
  • Youness EL YAZIDI,
  • Abdellatif ELLABIB
Youness EL YAZIDI
Cadi Ayyad University Faculty of Science and Technology Gueliz
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Abdellatif ELLABIB
Cadi Ayyad University Faculty of Science and Technology Gueliz
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Abstract

The aim of this paper is to construct a numerical scheme for solving a class of bilateral free boundaries problem. First, using a shape functional and some regularization terms, an optimal control problem is formulated, in addition, we prove its solution existence's. The first optimality conditions and the shape gradient are computed. the proposed numerical scheme is a genetic algorithm guided conjugate gradient combined with the finite element method, at each mesh regeneration, we perform a mesh refinement in order to avoid any domain singularities. Some numerical examples are shown to demonstrate the validity of the theoretical results, and to prove the robustness of the proposed scheme.

Peer review status:UNDER REVIEW

29 Jul 2020Submitted to Mathematical Methods in the Applied Sciences
31 Jul 2020Assigned to Editor
31 Jul 2020Submission Checks Completed
11 Aug 2020Reviewer(s) Assigned