A Time-Space Adaptive Method for the Schrödinger Equation. (22nd June 2016)

• Record Type: Journal Article
• Authors: Kormann, Katharina
• Is Part Of: Communications in computational physics. Volume 20:Number 1(2016:Jul.)
• Page Start: 60
• Page End: 85
• Publication Date: 2016-06-22
• Subjects: 65M50, -- 65M60, -- 65Z05, -- 81-08; a posteriori error estimate, -- adaptive mesh refinement, -- finite/spectral elements, -- time-dependent Schrödinger equation; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.101214.021015a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: In this paper, we present a discretization of the time-dependent Schrödinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in space. A truncated Galerkin orthogonality is used to obtain duality-based a posteriori error estimates that address the temporal and the spatial error separately. Based on this theory, a space-time adaptive solver for the Schrödinger equation is devised. An efficient matrix-free implementation of the differential operator, suited for spectral elements, is used to enable computations for realistic configurations. We demonstrate the performance of the algorithm for the example of matter-field interaction.