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Journal of Scientific Computing

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01.01.2021

A Level Set Method for the Dirichlet k-Partition Problem

verfasst von: Kwunlun Chu, Shingyu Leung

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2021

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Abstract

We propose a simple level set method for the Dirichlet k-partition problem which aims to partition an open domain into K different subdomains as to minimize the sum of the smallest eigenvalue of the Dirichlet Laplace operator in each subdomain. We first formulate the problem as a nested minimization problem of a functional of the level set function and the eigenfunction defined in each subdomain. As an approximation, we propose to simply replace the eigenfunction by the level set function so that the nested minimization can then be converted to a single minimization problem. We apply the standard gradient descent method so that the problem leads to a Hamilton–Jacobi type equation. Various numerical examples will be given to demonstrate the effectiveness of our proposed method.

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Titel: A Level Set Method for the Dirichlet k-Partition Problem
verfasst von: Kwunlun Chu
Shingyu Leung
Publikationsdatum: 01.01.2021
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2021
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01368-w

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