@Article{AAMM-7-687,
author = {Kieri , EmilKreiss , Gunilla and Runborg , Olof},
title = {Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrödinger Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {7},
number = {6},
pages = {687--714},
abstract = {<p style="text-align: justify;">In the semiclassical regime, solutions to the time-dependent Schr<span style="color: #333333; font-family: ">ö</span>dinger&nbsp; equation for molecular dynamics are highly oscillatory. The number of grid points
required for resolving the oscillations may become very large even for simple model
problems, making solution on a grid intractable. Asymptotic methods like Gaussian
beams can resolve the oscillations with little effort and yield good approximations
when the atomic nuclei are heavy and the potential is smooth. However, when the potential
has variations on a small length-scale, quantum phenomena become important.
Then asymptotic methods are less accurate. The two classes of methods perform well
in different parameter regimes. This opens for hybrid methods, using Gaussian beams
where we can and finite differences where we have to. We propose a new method for
treating the coupling between the finite difference method and Gaussian beams. The
new method reduces the needed amount of overlap regions considerably compared to
previous methods, which improves the efficiency.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2013.m411},
url = {http://global-sci.org/intro/article_detail/aamm/12071.html}
}