An efficient algorithm for solving the phase field crystal model

• Published in: Journal of computational physics Vol. 227; no. 12; pp. 6241 - 6248
• Main Authors: Cheng, Mowei, Warren, James A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.06.2008; Elsevier
• Subjects: ACCURACY; ALGORITHMS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; Computational techniques; COMPUTERIZED SIMULATION; CRYSTAL MODELS; DENSITY FUNCTIONAL METHOD; EQUATIONS; Exact sciences and technology; MATHEMATICAL EVOLUTION; Mathematical methods in physics; Phase field crystal model; Physics; Unconditionally stable; 81.15.Aa; 02.60.Cb; Unconditionally stable; 05.10.−a; 64.75.+g; Phase field crystal model; 05.10.-a; Algorithms; 81.15.Aa. Unconditionally stable: Phase field crystal model; Density functional method; 64.75.-g; Evolution equation; Models; Modelling; Calculation; Calculation methods
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2008.03.012

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.