A simple multiscale method for mean field games

This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates convergence and addresses problem determining initial guess. Starting from an approximate at coarsest level, constructs approximations on successively finer grids via alternating sweeping, not only allows use classical time marching schemes, but also enables applications to both local nonlocal problems. At each relaxation is used stabilize iterative process. A second-order discretization scheme derived higher order convergence. Numerical examples are provided demonstrate efficiency proposed in nonlocal, 1-dimensional 2-dimensional cases.