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This paper improves the convergence and robustness of a multigrid-basedsolver for the cross sections of the driven Schroedinger equation. Adding anCoupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycleefficiently removes the errors that remain after the V-cycle sweep. Thecombined iterative solution scheme (MG-CCCS) is shown to feature significantlyimproved convergence rates over the classical MG method at energies where boundstates dominate the solution, resulting in a fast and scalable solution methodfor the complex-valued Schroedinger break-up problem for any energy regime. Theproposed solver displays optimal scaling; a solution is found in a time that islinear in the number of unknowns. The method is validated on a 2D Temkin-Poetmodel problem, and convergence results both as a solver and preconditioner areprovided to support the O(N) scalability of the method. This paper extends theapplicability of the complex contour approach for far field map computation [S.Cools, B. Reps, W. Vanroose, An Efficient Multigrid Calculation of the FarField Map for Helmholtz and Schroedinger Equations, SIAM J. Sci. Comp. 36(3)B367--B395, 2014].

A fast and robust computational method for the ionization cross sections of the driven Schroedinger equation using an O(N) multigrid-based scheme