Linearly First- and Second-Order, Unconditionally Energy Stable Schemes for the Phase Field Crystal Model
In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank-Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposed schemes.
X. Yang and D. Han, "Linearly First- and Second-Order, Unconditionally Energy Stable Schemes for the Phase Field Crystal Model," Journal of Computational Physics, vol. 330, pp. 1116-1134, Academic Press Inc., Feb 2017.
The definitive version is available at https://doi.org/10.1016/j.jcp.2016.10.020
Mathematics and Statistics
Keywords and Phrases
Cahn-Hilliard; Linear scheme; Phase-field crystal; Second order; Unconditional energy stability
International Standard Serial Number (ISSN)
Article - Journal
© 2017 Academic Press Inc., All rights reserved.
01 Feb 2017