SOLUTION OF THE SYSTEMS ASSOCIATED WITH INVARIANT TORI APPROXIMATION .2. MULTIGRID METHODS

In this paper, the authors continue (see [Solution of the Systems Associated with Invariant Tori Approximation. I: Block Iterations and Compactifcation, manuscript, available from the first author]) the study of solution strategies for the linear systems arising from an upwind discretization of the periodic PDEs with same principal part associated with invariant tori. Here, multigrid approaches for the solution of these systems are considered. Several choices of smoothers are considered, and opportune choices of prolongations and restrictions are discussed. Some convergence results, as well as implementation details and numerical results for linear model problems are given. A nonlinear upwind discretization is discussed, and results are presented for the tori associated with two physically important nonlinear problems: the forced Josephson junction and a system of two coupled oscillators.