Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

Huang, He; Luo, Li -Shi; Li, Rui; Chen, Jie; Zhang, He

doi:10.1016/j.jcp.2018.05.028

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

Journal Article · Thu May 17 00:00:00 EDT 2018 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2018.05.028· OSTI ID:1439411

Huang, He ^[1]; Luo, Li -Shi ^[1]; Li, Rui ^[2]; Chen, Jie ^[2]; ^[2]

Old Dominion Univ., Norfolk, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 to 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.

Research Organization:: Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 1439411

Alternate ID(s):: OSTI ID: 1582863
OSTI ID: 23124953

Report Number(s):: DOE/OR/23177--4223; JLAB-ACP--17-2560; PII: S0021999118303280

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 371; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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A New Relatively Simple Approach to Multipole Interactions in Either Spherical Harmonics or Cartesians, Suitable for Implementation into Ewald Sums Burnham, Christian J.; English, Niall J. International Journal of Molecular Sciences, Vol. 21, Issue 1 https://doi.org/10.3390/ijms21010277	journal	December 2019