Thalmann Fabrice, Farago Jean
Institut Charles Sadron, CNRS UPR 22, 67083 Strasbourg Cedex, France, and Université Louis Pasteur, 4 rue Blaise Pascal, F-67070 Strasbourg Cedex, France.
J Chem Phys. 2007 Sep 28;127(12):124109. doi: 10.1063/1.2764481.
This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same "weak order two" accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.
本文聚焦于朗之万动力学的时间离散化以及由此产生的不同数值积分方案。我们采用基于含时算子指数运算的方法，精心推导了一种朗之万动力学的数值方案，发现它等同于埃尔马克和巴克霍兹[《计算物理杂志》35, 169 (1980)]提出的方案，而不仅仅等同于速度-Verlet算法的随机版本。然而，我们通过数值模拟检验发现，这两种算法给出的结果相似，且具有相同的“二阶弱精度”。然后，我们运用相同策略推导并测试了两种耗散粒子动力学的数值方案。结果发现，其中第一种方案在速度和精度方面与目前最好的算法相比毫不逊色。
