@inproceedings{8098360386dc40c0a1790392f41dbe37,
title = "Discrete Version of an Optimal Partitioning Problem",
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.",
keywords = "Eigenvalues, Finite differences, Numerical simulations, Optimal partitions",
author = "Beniamin Bogosel",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.; 23rd International Conference on Difference Equations and Applications, ICDEA 2017 ; Conference date: 24-07-2017 Through 28-07-2017",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-20016-9\_9",
language = "English",
isbn = "9783030200152",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "247--256",
editor = "Saber Elaydi and Christian P{\"o}tzsche and Sasu, \{Adina Lumini{\c t}a\}",
booktitle = "Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 23, 2017",
}