Fast, Unconditionally Energy Stable Large Time Stepping Method for a New Allen-Cahn Type Square Phase-Field Crystal Model
In this paper, we develop a new square phase-field crystal model using the L2-gradient flow approach, where the total mass of atoms is conserved through a nonlocal Lagrange multiplier. We construct a fast, provably unconditionally energy stable, second-order scheme by using the recently developed SAV approach with the stabilization technique, where an extra stabilization term is added to enhance the stability and keep the required accuracy while using large time steps. Through the comparisons with the classical Cahn-Hilliard type square phase-field crystal model and the non-stabilized SAV scheme for simulating some benchmark numerical examples, we demonstrate the robustness of the new model, as well as the stability and the accuracy of the developed scheme, numerically.
F. Lin et al., "Fast, Unconditionally Energy Stable Large Time Stepping Method for a New Allen-Cahn Type Square Phase-Field Crystal Model," Applied Mathematics Letters, vol. 98, pp. 248 - 255, Elsevier Ltd, Dec 2019.
The definitive version is available at https://doi.org/10.1016/j.aml.2019.06.007
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Linear; Phase-field crystal; Second-order; Stabilized-SAV; Unconditionally energy stable
International Standard Serial Number (ISSN)
Article - Journal
© 2019 Elsevier Ltd, All rights reserved.
01 Dec 2019