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

TL;DR

This paper introduces a numerical method based on a Γ-convergence approximation to study minimal partitions with anisotropic perimeters and explores isoperimetric problems with density.

Contribution

It provides a new theoretical Γ-convergence approximation and a numerical framework for analyzing anisotropic perimeter partitioning and isoperimetric problems with density.

Findings

Developed a Γ-convergence approximation for anisotropic length of partitions.

Created a numerical method for minimal partitions under anisotropic conditions.

Established a framework for isoperimetric problems with density.

Abstract

We present a ${\Gamma}$-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.