Fekete points in non-smooth surfaces

Abstract

In this paper we present a procedure for the estimation of the Fekete points on a wide variety of non-regular objects in $R^3$. We understand the problem of the Fekete points in terms of the identification of good equilibrium configurations for a potential energy that depends on the relative position of N particles. Although the procedure that we present here works well for different potential energies, the examples showed refer to the electrostatic potential energy, that plays an special role in Potential Theory and Physics. The objects for which our procedure has been designed can be described basically as the finite union of piecewise regular surfaces and curves. For the determination of a good starting configuration for the search of the Fekete points on such objects, a sequence of approximating regular surfaces must be constructed. The numerical experience carried out until now suggests that the total computational cost of the obtaining of a nearly optimal configuration with the procedure introduced here is less than $N^3$ independently of the object considered.