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BIT Numerical Mathematics

, Volume 50, Issue 1, pp 23–40 | Cite as

A regular fast multipole method for geometric numerical integrations of Hamiltonian systems

  • P. Chartier
  • E. Darrigrand
  • E. Faou
Article

Abstract

The Fast Multipole Method (FMM) has been widely developed and studied for the evaluation of Coulomb energy and Coulomb forces. A major problem occurs when the FMM is applied to approximate the Coulomb energy and Coulomb energy gradient within geometric numerical integrations of Hamiltonian systems considered for solving astronomy or molecular-dynamics problems: The FMM approximation involves an approximated potential which is not regular, implying a loss of the preservation of the Hamiltonian of the system. In this paper, we present a regularization of the Fast Multipole Method in order to recover the invariance of energy. Numerical tests are given on a toy problem to confirm the gain of such a regularization of the fast method.

Keywords

Hamiltonian system Geometric numerical integration Fast multipole method 

Mathematics Subject Classification (2000)

34A26 37J15 37M15 65P10 65Y20 

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Copyright information

© Springer Science + Business Media B.V. 2010

Authors and Affiliations

  1. 1.Equipe projet IPSOINRIA Rennes and Ecole Normale Supérieure de Cachan—Antenne de BretagneBruzFrance
  2. 2.IRMARUniversité de Rennes 1Rennes cedexFrance

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