dorsal/arxiv
View SchemaCommon Molecular Dynamics Algorithms Revisited: Accuracy and Optimal Time Steps of Stoermer-Leapfrog Integrators
| Authors | Alexey K. Mazur |
|---|---|
| Categories | |
| ArXiv ID | physics/9707008 |
| URL | https://arxiv.org/abs/physics/9707008 |
| DOI | 10.1006/jcph.1997.5740 |
| Journal | J. Comp. Phys. (1997) 136(2) 354-365. |
Abstract
The Stoermer-Verlet-leapfrog group of integrators commonly used in molecular dynamics simulations has long become a textbook subject and seems to have been studied exhaustively. There are, however, a few striking effects in performance of algorithms which are well-known but have not received adequate attention in the literature. A closer view of these unclear observations results in unexpected conclusions. It is shown here that contrary to the conventional point of view, the leapfrog scheme is distinguished in this group both in terms of the order of truncation errors and the conservation of the total energy. In this case the characteristic square growth of fluctuations of the total energy with the step size, commonly measured in numerical tests, results from additional interpolation errors with no relation to the accuracy of the computed trajectory. An alternative procedure is described for checking energy conservation of leapfrog-like algorithms which is free from interpolation errors. Preliminary tests on a representative model system suggest that standard step size values used at present are lower than necessary for accurate sampling.
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"abstract": "The Stoermer-Verlet-leapfrog group of integrators commonly used in molecular\ndynamics simulations has long become a textbook subject and seems to have been\nstudied exhaustively. There are, however, a few striking effects in performance\nof algorithms which are well-known but have not received adequate attention in\nthe literature. A closer view of these unclear observations results in\nunexpected conclusions. It is shown here that contrary to the conventional\npoint of view, the leapfrog scheme is distinguished in this group both in terms\nof the order of truncation errors and the conservation of the total energy. In\nthis case the characteristic square growth of fluctuations of the total energy\nwith the step size, commonly measured in numerical tests, results from\nadditional interpolation errors with no relation to the accuracy of the\ncomputed trajectory. An alternative procedure is described for checking energy\nconservation of leapfrog-like algorithms which is free from interpolation\nerrors. Preliminary tests on a representative model system suggest that\nstandard step size values used at present are lower than necessary for accurate\nsampling.",
"arxiv_id": "physics/9707008",
"authors": [
"Alexey K. Mazur"
],
"categories": [
"physics.comp-ph",
"physics.bio-ph",
"physics.chem-ph"
],
"doi": "10.1006/jcph.1997.5740",
"journal_ref": "J. Comp. Phys. (1997) 136(2) 354-365.",
"title": "Common Molecular Dynamics Algorithms Revisited: Accuracy and Optimal Time Steps of Stoermer-Leapfrog Integrators",
"url": "https://arxiv.org/abs/physics/9707008"
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