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Energy-momentum conserving integration schemes for molecular dynamics

Computational Mechanics volume 67, pages 915–935 (2021)Cite this article

Abstract

We address the formulation and analysis of energy and momentum conserving time integration schemes in the context of particle dynamics, and in particular atomic systems. The article identifies three critical aspects of these models that demand a careful analysis when discretized: first, the treatment of periodic boundary conditions; second, the formulation of approximations of systems with three-body interaction forces; third, their extension to atomic systems with functional potentials. These issues, and in particular their interplay with Energy-Momentum integrators, are studied in detail. Novel expressions for these time integration schemes are proposed and numerical examples are given to illustrate their performance.

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Notes

  1. https://lammps.sandia.gov.

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Acknowledgements

Support for M.S. was provided by the Deutsche Forschungsgemeinschaft (DFG) under Grant BE 2285/13-1 and the Research Travel Grant of the Karlsruhe House of Young Scientists (KYHS). This support is gratefully acknowledged.

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Authors and Affiliations

  1. Institut für Mechanik, Karlsruher Institut für Technologie, Gebäude 10.30, Otto-Ammann-Platz 9, 76131, Karlsruhe, Germany

    Mark Schiebl

  2. IMDEA Materials Institute, Eric Kandel 2, Tecnogetafe, 28906, Madrid, Spain

    Ignacio Romero

  3. Universidad Politécnica de Madrid, José Gutiérrez Abascal, 2, 28006, Madrid, Spain

    Ignacio Romero

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  1. Mark Schiebl
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  2. Ignacio Romero
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Correspondence to Ignacio Romero.

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Schiebl, M., Romero, I. Energy-momentum conserving integration schemes for molecular dynamics. Comput Mech 67, 915–935 (2021). https://doi.org/10.1007/s00466-020-01971-6

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  • DOI: https://doi.org/10.1007/s00466-020-01971-6

Keywords

  • Time integration
  • Conserving scheme
  • Molecular dynamics
  • Periodic boundary conditions