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A simple and efficient scheme for phase field crystalsimulation

Published online by Cambridge University Press:  30 July 2013

Matt Elsey
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York.. [email protected],[email protected]
Benedikt Wirth
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York.. [email protected],[email protected]
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Abstract

We propose an unconditionally stable semi-implicit time discretization of the phase fieldcrystal evolution. It is based on splitting the underlying energy into convex and concaveparts and then performing H-1 gradient descent steps implicitly for the formerand explicitly for the latter. The splitting is effected in such a way that the resultingequations are linear in each time step and allow an extremely simple implementation andefficient solution. We provide the associated stability and error analysis as well asnumerical experiments to validate the method’s efficiency.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2013

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