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

作者：Chartier P; Darrigrand E^*; Faou E

来源：BIT Numerical Mathematics, 2010, 50(1): 23-40.

DOI：10.1007/s10543-010-0248-6

• Hamiltonian system
• Geometric numerical integration
• Fast multipole method

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.

• 出版日期2010-3
• 单位INRIA