化学系统随机模拟辅助的自适应有限元方法
Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
AI总结：
提出一种利用化学系统随机模拟轨迹识别高概率密度区域，进而指导有限元网格自适应加密与粗化的方法，用于高效求解Fokker-Planck方程。
摘要：
化学系统的随机模型通常通过求解相应的Fokker-Planck方程进行分析，该方程是关于概率分布函数的漂移扩散偏微分方程。Fokker-Planck方程的高效数值求解需要自适应网格细化。在本文中，我们提出了一种网格细化方法，该方法利用底层化学系统的随机模拟。通过观察相对较短时间内的随机轨迹，识别出状态空间中具有不可忽略概率密度的区域。通过在这些区域细化有限元网格，并在其他地方粗化，构建出合适的网格，并用于概率密度的计算。
英文摘要：
Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with non-negligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the probability density.
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