# A simple and efficient scheme for phase field crystal simulation

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

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topElsey, 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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