论文标题
平均现场游戏的简单多尺度方法
A Simple Multiscale Method for Mean Field Games
论文作者
论文摘要
本文提出了一种求解平均现场游戏的数值解决方案的多尺度方法，该方法可以加速收敛并解决确定初始猜测的问题。从最高级别的近似解决方案开始，该方法通过交替的扫描构建近似细网格上的近似值，这不仅允许使用经典的时间行进数值方案，而且还可以将应用程序应用于本地和非局部问题。在每个级别，数值放松用于稳定迭代过程。为高阶收敛而得出了二阶离散方案。提供了数值示例，以证明在局部和非局部，一维和二维病例中提出的方法的效率。
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.
