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Treecode Algorithms for Computing Nonbonded Particle Interactions

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Computational Methods for Macromolecules: Challenges and Applications

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 24))

Abstract

Two new algorithms are described for computing nonbonded particle interactions in classical molecular systems, (1) a particle-cluster treecode for the real space Ewald sum in a system with periodic boundary conditions, and (2) a cluster-cluster treecode for the total potential energy in a system with vacuum boundary conditions. The first algorithm treats electrostatic interactions and the second algorithm treats general power-law interactions. Both algorithms use a divide-and-conquer strategy, adapted rectangular clusters, and Taylor approximation in Cartesian coordinates. The necessary Taylor coefficients are computed efficiently using recurrence relations. The second algorithm implements variable order approximation, and a run-time choice between Taylor approximation and direct summation. Test results are presented for an equilibrated water system, and random and sparse particle systems.

This work was supported by NSF grants DMS-9506452 and DMS-9973293, a University of Michigan Rackham Faculty Fellowship, and Michigan Life Sciences

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1109, USA

    Robert Krasny & Zhong-Hui Duan

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  1. Robert Krasny
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  2. Zhong-Hui Duan
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Editors and Affiliations

  1. Department of Chemistry, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Tamar Schlick  & Hin Hark Gan  & 

  2. Howard Hughes Medical Institute, 251 Mercer Street, New York, NY, 10012, USA

    Tamar Schlick  & Hin Hark Gan  & 

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Krasny, R., Duan, ZH. (2002). Treecode Algorithms for Computing Nonbonded Particle Interactions. In: Schlick, T., Gan, H.H. (eds) Computational Methods for Macromolecules: Challenges and Applications. Lecture Notes in Computational Science and Engineering, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56080-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-56080-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43756-7

  • Online ISBN: 978-3-642-56080-4

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