论文标题
具有随机数据的分数保护法的多级蒙特卡洛有限差异方法
Multi-level Monte Carlo Finite Difference Methods for Fractional Conservation Laws with Random Data
论文作者
论文摘要
我们建立了一个随机熵解决方案的概念，用于退化的分数保护法，该法律将随机性纳入初始数据，对流通量和扩散通量。为了量化溶液不确定性，我们设计了一种多级蒙特卡洛有限差异方法（MLMC-FDM），以近似随机熵溶液的整体平均值。此外，我们分析了MLMC-FDM的收敛速率，并将其与确定性情况的收敛速率进行比较。此外，我们制定了多级估计器的错误与工作估计。最后，我们提出了几个数值实验，以证明这些方案的效率并验证本工作中获得的理论估计值。
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In order to quantify the solution uncertainty, we design a multi-level Monte Carlo Finite Difference Method (MLMC-FDM) to approximate the ensemble average of the random entropy solutions. Furthermore, we analyze the convergence rates for MLMC-FDM and compare it with the convergence rates for the deterministic case. Additionally, we formulate error vs. work estimates for the multi-level estimator. Finally, we present several numerical experiments to demonstrate the efficiency of these schemes and validate the theoretical estimates obtained in this work.
