Variational collision integrator for polymer chains
Leyendecker S, Koch M, Hartmann C (2012)
Publication Type: Journal article, Original article
Publication year: 2012
Journal
Publisher: Elsevier
DOI: 10.1016/j.jcp.2012.01.017
Abstract
The numerical simulation of many-particle systems (e.g. in molecular dynamics) often involves constraints of various forms. We present a symplectic integrator for mechanical systems with holonomic (bilateral) and unilateral contact constraints, the latter being in the form of a non-penetration condition. The scheme is based on a discrete variant of Hamilton's principle in which both the discrete trajectory and the unknown collision time are varied (cf. [R. Fetecau, J. Marsden, M. Ortiz, M. West, Nonsmooth Lagrangian mechanics and variational collision integrators, SIAM J. Appl. Dyn. Syst. 2 (2003) 381-416]). As a consequence, the collision event enters the discrete equations of motion as an unknown that has to be computed on-the-fly whenever a collision is imminent. The additional bilateral constraints are efficiently dealt with employing a discrete null space reduction (including a projection and a local reparametrisation step) which considerably reduces the number of unknowns and improves the condition number during each time-step as compared to a standard treatment with Lagrange multipliers. We illustrate the numerical scheme with a simple example from polymer dynamics, a linear chain of beads, and test it against other standard numerical schemes for collision problems. © 2012 Elsevier Inc.
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APA:
Leyendecker, S., Koch, M., & Hartmann, C. (2012). Variational collision integrator for polymer chains. Journal of Computational Physics. https://doi.org/10.1016/j.jcp.2012.01.017
MLA:
Leyendecker, Sigrid, Michael Koch, and Carsten Hartmann. "Variational collision integrator for polymer chains." Journal of Computational Physics (2012).
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