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Delfour, M.C. (2018) Topological Derivative: A Semidifferential via the Minkowski Content. Journal of Convex Analysis, 3, 957-982.

has been cited by the following article:

• TITLE: Descent Topological Gradient Optimization Algorithm Applied to 1D and 2D Charged Photonic Crystals

  AUTHORS: Mouhamadou Baïdy Dia, Ibrahima Sagno, Malick Fall, Lansana Toure, Mouctar Ndiaye

  KEYWORDS: Photonic Crystals, Band Gap, Topological Optimization, Min-Max Principle, Electromagnetic, Elastic and Acoustic Waves, Topological Derivatives, Finite Elements, FreeFEM

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.7, July 29, 2025

  ABSTRACT: The aim of this research article is to apply topological optimization gradient algorithm applied to 1D and 2D photonic charged slabs. We compute the topological gradient using min max method. We use an iterative algorithm for descending the topological gradient and with steps as the radius of circular holes, implemented under FreeFEM with the finite elements’ method.