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Elliptic Fekete points obtained by Ginzburg-Landau PDE

Jezdimirovic, Jovana, Alexandre Chemin, Pierre-Alexandre Beaufort, Jean-François Remacle

Research Notes, 26th International Meshing Roundtable, Sandia National Laboratories, September 18-21 2017


26th International Meshing Roundtable
Barcelona, Spain
September 18-21, 2017

Jovana Jezdimirovic, Université catholique de Louvain, BE,
Alexandre Chemin, Université catholique de Louvain, BE,
Pierre-Alexandre Beaufort, Université catholique de Louvain, BE,
Jean-François Remacle, Université catholique de Louvain, BE,

Research Note Abstract
The aim of the paper is to present solutions of Thomson’s problem i.e. the determination of the minimum potential energy location of N points x i , i = 1, . . . , N on the 2-sphere. The specific case that is treated here is the Fekete problem where points repel each other with a force that depends on the logarithm of their respective distance. This paper presents a method to compute Fekete points by solving a partial differential equation that is usually used for computing cross fields. This approach is quite uncommon and quite competitive for N large.

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