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A simple and efficient scheme for phase field crystal simulation∗

Published online by Cambridge University Press:  30 July 2013

Matt Elsey  and
Benedikt Wirth
Matt Elsey
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York.. melsey@cims.nyu.edu,benedikt.wirth@cims.nyu.edu
Benedikt Wirth
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York.. melsey@cims.nyu.edu,benedikt.wirth@cims.nyu.edu
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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.

Keywords

Phase field crystalsemi-implicit time discretizationconvex-concave splitting
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 5 , September 2013 , pp. 1413 - 1432
Copyright
© EDP Sciences, SMAI, 2013

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