Variational collision integrator for polymer chains

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• 作者：Sigrid Leyendecker^a ; ^{sigrid.leyendecker@ltd.uni-erlangen.de} ; Carsten Hartmann^b ; Michael Koch^a
• 关键词：Variational integrators ; Collisions ; Holonomic constraints ; Discrete null space method ; Event-driven algorithm ; Polymer dynamics ; Chain of beads
• 刊名：Journal of Computational Physics
• 出版年：2012
• 期刊代码：136_00219991
• 类别：cp
• 出版时间：20 May, 2012
• 卷：231
• 期：10
• 页码：3896-3911
• 文件大小：1449 K

摘要

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鈥檚 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.