Optimal design of sensors via geometric criteria
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Fecha
2023-05-23
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Springer
Resumen
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.
Palabras clave
Convex geometry
Sensor design
Shape optimization
Sensor design
Shape optimization
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Materias
Cita
Ftouhi, I., & Zuazua, E. (2023). Optimal design of sensors via geometric criteria. Journal of Geometric Analysis, 33(8). https://doi.org/10.1007/S12220-023-01301-1