A simple and efficient scheme for phase field crystal simulation

Matt Elsey; Benedikt Wirth

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 5, page 1413-1432
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Elsey, Matt, and Wirth, Benedikt. "A simple and efficient scheme for phase field crystal simulation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.5 (2013): 1413-1432. <http://eudml.org/doc/273322>.

@article{Elsey2013,
abstract = {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.},
author = {Elsey, Matt, Wirth, Benedikt},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {phase field crystal; semi-implicit time discretization; convex-concave splitting; embedding; convergence},
language = {eng},
number = {5},
pages = {1413-1432},
publisher = {EDP-Sciences},
title = {A simple and efficient scheme for phase field crystal simulation},
url = {http://eudml.org/doc/273322},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 5
SP - 1413
EP - 1432
AB - 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.
LA - eng
KW - phase field crystal; semi-implicit time discretization; convex-concave splitting; embedding; convergence
UR - http://eudml.org/doc/273322
ER -

References

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