Year: 2016
Communications in Computational Physics, Vol. 20 (2016), Iss. 1 : pp. 60–85
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.101214.021015a
Communications in Computational Physics, Vol. 20 (2016), Iss. 1 : pp. 60–85
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26