平均场对策的一种简单多尺度方法
A Simple Multiscale Method for Mean Field Games
摘要：
本文提出了一种求解平均场对策数值解的多尺度方法，该方法加速了收敛，并解决了初始猜想的确定问题。从一个近似解在粗层次上，该方法通过交替扫描，这不仅允许使用经典的时间推进数值方案，但也使本地和非本地问题的应用程序上的连续更精细的网格构造近似。在每一层，数值松弛被用来稳定迭代过程。一个二阶离散格式推导出高阶收敛。数值算例表明，所提出的方法在局部和非局部，1维和2维的情况下的效率。
英文摘要：
This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the coarsest level, the method constructs approximations on successively finer grids via alternating sweeping, which not only allows for the use of classical time marching numerical schemes but also enables applications to both local and nonlocal problems. At each level, numerical relaxation is used to stabilize the iterative process. A second-order discretization scheme is derived for higher-order convergence. Numerical examples are provided to demonstrate the efficiency of the proposed method in both local and nonlocal, 1-dimensional and 2-dimensional cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
