A fast and robust computational method for the ionization cross sections of the driven Schrödinger equation using an O(N)multigrid-based schemeA fast and robust computational method for the ionization cross sections of the driven Schrödinger equation using an O(N)multigrid-based scheme
Faculty of Sciences. Mathematics and Computer Science
Applied mathematics and numerical analysis
2016New York, 2016
Journal of computational physics. - New York
308(2016), p. 20-39
University of Antwerp
This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schrödinger equation. Adding a Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently removes the errors that remain after the V-cycle sweep. The combined iterative solution scheme (MG-CCCS) is shown to feature significantly improved convergence rates over the classical MG method at energies where bound states dominate the solution, resulting in a fast and scalable solution method for the complex-valued Schrödinger break-up problem for any energy regime. The proposed solver displays optimal scaling; a solution is found in a time that is linear in the number of unknowns. The method is validated on a 2D TemkinPoet model problem, and convergence results both as a solver and preconditioner are provided to support the O(N)O(N) scalability of the method. This paper extends the applicability of the complex contour approach for far field map computation (Cools et al. (2014) ).