A regular fast multipole method for geometric numerical integrations of Hamiltonian systems
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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.
KeywordsHamiltonian system Geometric numerical integration Fast multipole method
Mathematics Subject Classification (2000)34A26 37J15 37M15 65P10 65Y20
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