论文标题
蒙特卡洛随机galerkin方法，用于具有不确定性的多种基因系统的非马克斯威尔动力学模型
Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties
论文作者
论文摘要
在本文中，我们着重于建立一个混合方案，以近似具有不确定性的非麦克斯韦动力学模型。在多基因系统的背景下，在动力学水平上引入核对避免非物理相互作用很有用。此处提出的方法将直接模拟的蒙特卡洛（DSMC）与随机空间中的随机盖尔金（SG）方法结合在一起。开发的方案将溶液的主要物理特性保留在随机空间中的精度。该方法的一致性是针对可以在准参数的准不变制度中获得的替代Fokker-Planck模型的。报告了该方案对多轴心系统的非马克斯威尔模型的几种应用。
In this paper, we focus on the construction of a hybrid scheme for the approximation of non-Maxwellian kinetic models with uncertainties. In the context of multiagent systems, the introduction of a kernel at the kinetic level is useful to avoid unphysical interactions. The methods here proposed, combine a direct simulation Monte Carlo (DSMC) in the phase space together with stochastic Galerkin (sG) methods in the random space. The developed schemes preserve the main physical properties of the solution together with accuracy in the random space. The consistency of the methods is tested with respect to surrogate Fokker-Planck models that can be obtained in the quasi-invariant regime of parameters. Several applications of the schemes to non-Maxwellian models of multiagent systems are reported.
