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