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Multilevel Monte Carlo method for the Brownian configuration field of polymer fluids
Aip Advances ( IF 1.6 ) Pub Date : 2020-09-10 , DOI: 10.1063/5.0023398 Jin Su 1 , Cuihong Hou 1 , Yingcang Ma 1 , Yaowu Wang 2
Aip Advances ( IF 1.6 ) Pub Date : 2020-09-10 , DOI: 10.1063/5.0023398 Jin Su 1 , Cuihong Hou 1 , Yingcang Ma 1 , Yaowu Wang 2
Affiliation
Stochastic Brownian dynamics is an extremely powerful way to simulate the polymer dynamics in solutions and melts. Mathematically, these models are described by stochastic differential equations. The most challenging problems are the Monte Carlo algorithm, which simulates the motion of a large number of model particles and hence requires an enormous amount of computer time. It is therefore necessary to develop an efficient numerical method in operational emergency response applications. In this paper, we give an improved multilevel Monte Carlo (improved-MLMC) method based on equilibrium control variables at each level to calculate the propagation of polymers. The improved-MLMC method can be shown to result in asymptotically optimal random errors and reduce total cost when compared to the standard Monte Carlo and MLMC methods. Finally, the effect of the Wi number (dimensionless parameter) on the total cost of the presented MLMC method is also discussed in detail.
中文翻译:
聚合物流体布朗组态领域的多级蒙特卡罗方法
随机布朗动力学是一种非常强大的方法,可以模拟溶液和熔体中的聚合物动力学。在数学上,这些模型由随机微分方程描述。最具挑战性的问题是蒙特卡洛算法,该算法可模拟大量模型粒子的运动,因此需要大量的计算机时间。因此,有必要在操作应急应用中开发一种有效的数值方法。在本文中,我们基于每个级别的平衡控制变量,给出了一种改进的多级蒙特卡洛(improved-MLMC)方法,以计算聚合物的扩散。与标准的蒙特卡洛方法和MLMC方法相比,改进的MLMC方法可显示出渐近最优随机误差并降低总成本。最后,还详细讨论了所提出的MLMC方法总成本的Wi数(无因次参数)。
更新日期:2020-09-30
中文翻译:
聚合物流体布朗组态领域的多级蒙特卡罗方法
随机布朗动力学是一种非常强大的方法,可以模拟溶液和熔体中的聚合物动力学。在数学上,这些模型由随机微分方程描述。最具挑战性的问题是蒙特卡洛算法,该算法可模拟大量模型粒子的运动,因此需要大量的计算机时间。因此,有必要在操作应急应用中开发一种有效的数值方法。在本文中,我们基于每个级别的平衡控制变量,给出了一种改进的多级蒙特卡洛(improved-MLMC)方法,以计算聚合物的扩散。与标准的蒙特卡洛方法和MLMC方法相比,改进的MLMC方法可显示出渐近最优随机误差并降低总成本。最后,还详细讨论了所提出的MLMC方法总成本的Wi数(无因次参数)。