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Alireza Fakharzadeh Jahromi Hajar Alimorad Dastkhezr Ali Beiranvand

Abstract

‎Considering a damped wave system defined on a two-dimensional domain‎, ‎with a dissipative term localized in an unknown subset with an unknown damping parameter‎, ‎we address the shape design ill-posed problem which consists of optimizing the shape of the unknown subset in order to minimize the energy of the system at a given time‎. ‎By using a new approach based on the embedding process‎, ‎first‎, ‎the system is formulated in variational form; then‎, ‎by transferring the problem into polar coordinates and defining two positive Radon measures‎, ‎we represent the problem in a space of measures‎. ‎In this way‎, ‎the shape design problem is changed into an infinite linear one whose solution is guaranteed‎. ‎In this stage‎, ‎by applying two subsequent approximation steps‎, ‎the optimal solution (optimal control‎, ‎optimal region‎, ‎optimal damping parameter and optimal energy) is identified by a three-phase optimization search technique‎. ‎Numerical simulations are also given in order to compare this new method with another one‎.

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How to Cite
Fakharzadeh JahromiA., Alimorad DastkhezrH., & BeiranvandA. (2016). A Linearization Technique for Optimal Design of the Damping Set with Internal Dissipation. Iranian Journal of Numerical Analysis and Optimization, 6(1), 1-31. https://doi.org/10.22067/ijnao.v6i1.44335
Section
Research Article