Comparison between shape optimization and volumic level set approximation for geometrical functionals

2008/06/07 by Thomas Milcent, Milcent, T.
Computer Science · Engineering · #3D Shape Modeling and Analysis #65K10 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.0806.1288

openalex publication_date 2008/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We propose to differentiate a general curvature functional with two different approaches. In the first one we compute the derivative with the tools of shape optimization and in the second one we compute the derivative of a volumic approximation of the functional with respect to a level set function. We show that the two previous approaches give the same result.

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