An efficient algorithm for solving the phase field crystal model

Authors:
Mowei Cheng;James A. Warren
Affiliations:
Metallurgy Division and Center for Theoretical and Computational Materials Science, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA;Metallurgy Division and Center for Theoretical and Computational Materials Science, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

We present and discuss the development of an unconditionally stable algorithm used to solve the evolution equations of the phase field crystal (PFC) model. This algorithm allows for an arbitrarily large algorithmic time step. As the basis for our analysis of the accuracy of this algorithm, we determine an effective time step in Fourier space. We then compare our calculations with a set of representative numerical results, and demonstrate that this algorithm is an effective approach for the study of the PFC models, yielding a time step effectively 180 times larger than the Euler algorithm for a representative set of material parameters. As the PFC model is just a simple example of a wide class of density functional theories, we expect this method will have wide applicability to modeling systems of considerable interest to the materials modeling communities.