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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:308

Article

Cools, S.¹  Vanroose, W.¹ 

[1] Univ Antwerp, Dept Math & Comp Sci, Appl Math Res Grp, Middelheimlaan 1, B-2020 Antwerp, Belgium

关键词: Schrodinger equation;    Cross sections;    Complex contour;    Multigrid;    Coupled channel correction scheme;    Temkin-Poet;   

DOI  :  10.1016/j.jcp.2015.12.019

来源: Elsevier

【 摘 要 】

This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schrodinger 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 Schrodinger 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 Temkin-Poet model problem, and convergence results both as a solver and preconditioner are provided to support the 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) [10]). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free