A semi-analytical approach to molecular dynamics

Dominik L. Michels*, Mathieu Desbrun

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Despite numerous computational advances over the last few decades, molecular dynamics still favors explicit (and thus easily-parallelizable) time integrators for large scale numerical simulation. As a consequence, computational efficiency in solving its typically stiff oscillatory equations of motion is hampered by stringent stability requirements on the time step size. In this paper, we present a semi-analytical integration scheme that offers a total speedup of a factor 30 compared to the Verlet method on typical MD simulation by allowing over three orders of magnitude larger step sizes. By efficiently approximating the exact integration of the strong (harmonic) forces of covalent bonds through matrix functions, far improved stability with respect to time step size is achieved without sacrificing the explicit, symplectic, time-reversible, or fine-grained parallelizable nature of the integration scheme. We demonstrate the efficiency and scalability of our integrator on simulations ranging from DNA strand unbinding and protein folding to nanotube resonators.

Original languageEnglish (US)
Pages (from-to)336-354
Number of pages19
JournalJournal of Computational Physics
StatePublished - Dec 15 2015
Externally publishedYes


  • Energy conservation
  • Explicit integration
  • Exponential integrators
  • Fast Multipole Method
  • Krylov subspace projection
  • Molecular dynamics
  • Momentum conservation
  • Symplectic integrators

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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