Geodesic
Longest minimal length partitions
Beniamin Bogosel1 ; Édouard Oudet2
1École Polytechnique, Palaiseau, France
2Université Grenoble Alpes, France
Interfaces and free boundaries, Tome 24 (2022) no. 1, pp. 95-135

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DOI

This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which performs multiple optimization steps at each iteration to approximate minimal partitions. Using these partitions we compute perturbations of the domain which increase the minimal perimeter. The initialization of the optimal partitioning algorithm uses capacity-constrained Voronoi diagrams. A new algorithm is proposed to identify such diagrams, by computing the gradients of areas and perimeters for the Voronoi cells with respect to the Voronoi points.
DOI : 10.4171/ifb/468
Classification : 49-XX
Mots-clés : Optimal partitions, shape optimization, numerical simulations, isoperimetric problems

Beniamin Bogosel  1   ; Édouard Oudet  2

1 École Polytechnique, Palaiseau, France
2 Université Grenoble Alpes, France 
Beniamin Bogosel; Édouard Oudet. Longest minimal length partitions. Interfaces and free boundaries, Tome 24 (2022) no. 1, pp. 95-135. doi: 10.4171/ifb/468
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     year = {2022},
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     number = {1},
     doi = {10.4171/ifb/468},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/468/}
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