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An Efficient Algorithm for Solving the Phase Field Crystal Model



Mowei Cheng, James A. Warren


We present and discuss the development an unconditionally stable algorithm to solving the evolution equations for 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 180 times larger than the Euler algorithm for a representative set of materials 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.
Journal of Computational Physics


algorithm, Phase Field Crystal (PFC), unconditionally stable algorithm


Cheng, M. and Warren, J. (2008), An Efficient Algorithm for Solving the Phase Field Crystal Model, Journal of Computational Physics (Accessed July 12, 2024)


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Created June 1, 2008, Updated June 2, 2021