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Pré-Publication, Document De Travail Année : 2020

On a shape derivative formula for a family of star-shaped domains

Résumé

In this work, we consider again the shape derivative formula for a volume cost functional which we studied in preceding papers where we used the Minkowski deformation and the support functions in the convex setting. Here, we extend it to some non convex domains, namely the star-shaped ones. The formula also happens to be an extension of a well known formula in the Brunn-Minkowski theory. Finally, we illustrate the formula by applying it to the computation of the shape derivative for a shape optimization problem and by giving an algorithm based on the gradient method.
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Dates et versions

hal-02084874 , version 1 (29-03-2019)
hal-02084874 , version 2 (15-01-2020)
hal-02084874 , version 3 (17-10-2021)
hal-02084874 , version 4 (07-03-2023)

Identifiants

  • HAL Id : hal-02084874 , version 2

Citer

A. Boulkhemair, A. Chakib, A Sadik. On a shape derivative formula for a family of star-shaped domains. 2020. ⟨hal-02084874v2⟩
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