We propose an unconditionally stable semi-implicit time discretization of the phase field crystal evolution. It is based on splitting the underlying energy into convex and concave parts and then performing H-1 gradient descent steps implicitly for the former and explicitly for the latter. The splitting is effected in such a way that the resulting equations are linear in each time step and allow an extremely simple implementation and efficient solution. We provide the associated stability and error analysis as well as numerical experiments to validate the method's efficiency.
Mots-clés : phase field crystal, semi-implicit time discretization, convex-concave splitting
@article{M2AN_2013__47_5_1413_0,
author = {Elsey, Matt and Wirth, Benedikt},
title = {A simple and efficient scheme for phase field crystal simulation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1413--1432},
publisher = {EDP-Sciences},
volume = {47},
number = {5},
year = {2013},
doi = {10.1051/m2an/2013074},
mrnumber = {3100769},
zbl = {1286.74118},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2013074/}
}
TY - JOUR AU - Elsey, Matt AU - Wirth, Benedikt TI - A simple and efficient scheme for phase field crystal simulation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1413 EP - 1432 VL - 47 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013074/ DO - 10.1051/m2an/2013074 LA - en ID - M2AN_2013__47_5_1413_0 ER -
%0 Journal Article %A Elsey, Matt %A Wirth, Benedikt %T A simple and efficient scheme for phase field crystal simulation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1413-1432 %V 47 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013074/ %R 10.1051/m2an/2013074 %G en %F M2AN_2013__47_5_1413_0
Elsey, Matt; Wirth, Benedikt. A simple and efficient scheme for phase field crystal simulation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 5, pp. 1413-1432. doi : 10.1051/m2an/2013074. http://www.numdam.org/articles/10.1051/m2an/2013074/
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