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Discrete Version of an Optimal Partitioning Problem

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Difference Equations, Discrete Dynamical Systems and Applications (ICDEA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 287))

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Abstract

Many recent works deal with problems concerning optimal partitions related to spectral quantities of domains in Euclidean spaces or on manifolds. Due to the complexity of these problems, few explicit solutions are known. Therefore, numerical algorithms have been developed in order to find approximations of optimal partitions. Such algorithms are based on discretizations of the domain and lead to finite dimensional difference equations. In the following, the coupling of the gradient descent method with a projection algorithm leads to a non-linear difference equation. Various properties of the discrete problem are discussed and numerical results illustrating the behaviour of the discretization scheme are shown.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées, École Polytechnique, Palaiseau, France

    Beniamin Bogosel

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  1. Beniamin Bogosel
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Correspondence to Beniamin Bogosel .

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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

  2. Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Klagenfurt, Austria

    Christian Pötzsche

  3. Department of Mathematics, West University of Timişoara, Timişoara, Romania

    Adina Luminiţa Sasu

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Bogosel, B. (2019). Discrete Version of an Optimal Partitioning Problem. In: Elaydi, S., Pötzsche, C., Sasu, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 287. Springer, Cham. https://doi.org/10.1007/978-3-030-20016-9_9

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