This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schrödinger equation in the semiclassical limit. We specifically analyse the convergence behavior of the first-order splitting. Our main result is a proof of uniform accuracy. We illustrate the properties of our methods with simulations.
Accepté le :
DOI : 10.1051/m2an/2018060
Mots-clés : Schrödinger equation, semiclassical limit, numerical simulation, uniformly accurate, Madelung transform, splitting schemes
@article{M2AN_2019__53_2_443_0,
author = {Chartier, Philippe and Le Treust, Lo{\"\i}c and M\'ehats, Florian},
title = {Uniformly accurate time-splitting methods for the semiclassical linear {Schr\"odinger} equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {443--473},
publisher = {EDP-Sciences},
volume = {53},
number = {2},
year = {2019},
doi = {10.1051/m2an/2018060},
zbl = {1431.35166},
mrnumber = {3942175},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2018060/}
}
TY - JOUR AU - Chartier, Philippe AU - Le Treust, Loïc AU - Méhats, Florian TI - Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2019 SP - 443 EP - 473 VL - 53 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2018060/ DO - 10.1051/m2an/2018060 LA - en ID - M2AN_2019__53_2_443_0 ER -
%0 Journal Article %A Chartier, Philippe %A Le Treust, Loïc %A Méhats, Florian %T Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2019 %P 443-473 %V 53 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2018060/ %R 10.1051/m2an/2018060 %G en %F M2AN_2019__53_2_443_0
Chartier, Philippe; Le Treust, Loïc; Méhats, Florian. Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 2, pp. 443-473. doi : 10.1051/m2an/2018060. http://www.numdam.org/articles/10.1051/m2an/2018060/
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