@Article{CiCP-20-60,
author = {Katharina Kormann},
title = {A Time-Space Adaptive Method for the Schrödinger Equation},
journal = {Communications in Computational Physics},
year = {2018},
volume = {20},
number = {1},
pages = {60--85},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.101214.021015a},
url = {http://global-sci.org/intro/article_detail/cicp/11145.html}
}