Longest minimal length partitions

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 a...

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Published in:Interfaces and free boundaries 2022-03, Vol.24 (1), p.95-135
Main Authors: Bogosel, Beniamin, Oudet, Edouard
Format: Article
Language:English
Subjects:
Algorithms
Mathematical optimization
Mathematical research
Mathematics
Optimization and Control
Partitions (Mathematics)
Perturbation (Mathematics)
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Oudet, Edouard
description 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.
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subjects Algorithms
Mathematical optimization
Mathematical research
Mathematics
Optimization and Control
Partitions (Mathematics)
Perturbation (Mathematics)
title Longest minimal length partitions
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