Examinando por Autor "Ftouhi, Ilias"

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  • Miniatura
    Ítem
    Optimal design of sensors via geometric criteria
    (Springer, 2023-05-23) Ftouhi, Ilias; Zuazua, Enrique
    We consider a convex set Ω and look for the optimal convex sensor ω⊂ Ω of a given measure that minimizes the maximal distance to the points of Ω. This problem can be written as follows inf{dH(ω,Ω)||ω|=candω⊂Ω}, where c∈ (0 , | Ω |) , dH being the Hausdorff distance. We show that the parametrization via the support functions allows us to formulate the geometric optimal shape design problem as an analytic one. By proving a judicious equivalence result, the shape optimization problem is approximated by a simpler minimization problem of a quadratic function under linear constraints. We then present some numerical results and qualitative properties of the optimal sensors and exhibit an unexpected symmetry breaking phenomenon.
  • Miniatura
    Ítem
    Sensor placement via large deviations in the Eikonal equation
    (Springer Science and Business Media Deutschland GmbH, 2026-03-11) Ftouhi, Ilias; Zuazua, Enrique
    In this work, we address the problem of optimally placing a finite number of sensors within a given region so as to minimize the mean or maximal distance to the points of the domain. To tackle this natural geometric performance criterion, formulated in terms of distance functions, we combine tools from geometric analysis with a classical result of Varadhan (Commun Pure Appl Math 20:431–455, 1967), which provides an efficient approximation of the distance function via the solution of a simple elliptic PDE. The effectiveness of the proposed approach is demonstrated through illustrative numerical simulations.