Numerical study of optimal partitioning problems in relation to an anisotropic perimeter

2016/09/06 by Beniamin Bogosel, Bogosel, Beniamin
Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematical Approximation and Integration #Optimization and Control (math.OC) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1609.01467

openalex publication_date 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a Γ-convergence approximation for the total anisotropic length of a partition. This theoretical result gives rise to a numerical method which allows the study of minimal partitions with respect to different anisotropies. We also give a numerical framework for the study of isoperimetric problems with density.

Related

• On the anisotropic partitioning problem in Euclidean convex domains
• Finite variations on the isoperimetric problem
• Monotonicity of the optimal perimeter in isoperimetric problems on ℤ^k × ℕ^d
• Anisotropic perimeter and isoperimetric quotient of inner parallel bodies
• Longest minimal length partitions