Fekete Points in non-Smooth Surfaces Enrique Bendito, ´ Angeles Carmona, Andr´ es M. Encinas and Jos´ e M. Gesto Departament de Matem` atica Aplicada III Universitat Polit` ecnica de Catalunya. Espa˜ na Abstract In this paper we present a procedure for the estimation of the Fekete points on a wide variety of non-regular objects in IR 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 deter- mination 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 compu- tational cost of the obtaining of a nearly optimal configuration with the procedure introduced here is less than N 3 independently of the object considered. 1 Introduction The N -th order Fekete points of a compact set K ⊂ IR d are N -tuples ω N = {x 1 ,...,x N } of points x i ∈ K minimizing a functional of the form I (ω N )=  1≤i<j ≤N K(x i ,x j ), where K is a lower semicontinuous function called kernel. The functional I is usually called the potential energy associated with K. The kernel K can adopt multiple forms. For instance, if |x i − x j | is the Euclidean distance between x i and x j , the logarithmic kernel, K(x i ,x j )= − ln |x i −x j | and the Riesz’s kernels, K(x i ,x j )= |x i −x j | -s ,s> 0, are the most treated in the literature. In the three-dimensional space, these concepts play an important role in Physics, where they can be interpreted in different ways. From a mechanical point of view, if I is the 1