TY - JOUR
T1 - A semi-analytical approach to molecular dynamics
AU - Michels, Dominik L.
AU - Desbrun, Mathieu
N1 - Funding Information:
The authors are grateful to Ryan S. Elliott, Dennis M. Kochmann, and Ellad B. Tadmor for helpful discussions, as well as J. Paul T. Mueller for his help with the visualizations. This work has been partially supported by the Max Planck Center for Visual Computing and Communication funded by the Federal Ministry of Education and Research of the Federal Republic of Germany ( FKZ-01IMC01 and FKZ-01IM10001 ) and the National Science Foundation of the United States of America ( CCF-1011944 ). Furthermore, the authors gratefully acknowledge the helpful suggestions and comments from the anonymous reviewers.
Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015/12/15
Y1 - 2015/12/15
N2 - 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.
AB - 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.
KW - Energy conservation
KW - Explicit integration
KW - Exponential integrators
KW - Fast Multipole Method
KW - Krylov subspace projection
KW - Molecular dynamics
KW - Momentum conservation
KW - Symplectic integrators
UR - http://www.scopus.com/inward/record.url?scp=84944227979&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2015.10.009
DO - 10.1016/j.jcp.2015.10.009
M3 - Article
AN - SCOPUS:84944227979
SN - 0021-9991
VL - 303
SP - 336
EP - 354
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -
