Numerical Approximation of Optimal Convex Shapes
نویسندگان
چکیده
منابع مشابه
Optimal convex shapes for concave functionals
Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and ind...
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We focus here on the analysis of the regularity or singularity of solutions Ω0 to shape optimization problems among convex planar sets, namely: J(Ω0) = min{J(Ω), Ω convex, Ω ∈ Sad}, where Sad is a set of 2-dimensional admissible shapes and J : Sad → R is a shape functional. Our main goal is to obtain qualitative properties of these optimal shapes by using first and second order optimality condi...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2020
ISSN: 1064-8275,1095-7197
DOI: 10.1137/19m1256853