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A Particle Clustering Algorithm for the Fast Evaluation of Coulomb-type Potentials in R 3

We present a simple method for the fast evaluation of Coulomb-type potential induced by point sources. The method is based upon a hierarchical structuring of the particles and a local approximation of the potential by the use of an addition theorem. The costs of the algorithm are O(p 2 n log n), where n is the number of particles and p is related to the accuracy of the evaluation by p = O(j log(")j). The method is inherently adaptive and reasonably easy to implement.