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Title: Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

Abstract

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.

Authors:
 [1];  [2]
  1. Department of Mathematics, University of South Carolina, Columbia, SC 29208 (United States)
  2. Department of Mathematics, Indiana University at Bloomington (United States)
Publication Date:
OSTI Identifier:
22622255
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 330; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; COMPUTERIZED SIMULATION; CRYSTAL FIELD; CRYSTAL MODELS; CRYSTALS; EFFICIENCY; EQUATIONS; STABILITY; SYMMETRY; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu, and Han, Daozhi, E-mail: djhan@iu.edu. Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2016.10.020.
Yang, Xiaofeng, E-mail: xfyang@math.sc.edu, & Han, Daozhi, E-mail: djhan@iu.edu. Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model. United States. doi:10.1016/J.JCP.2016.10.020.
Yang, Xiaofeng, E-mail: xfyang@math.sc.edu, and Han, Daozhi, E-mail: djhan@iu.edu. Wed . "Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model". United States. doi:10.1016/J.JCP.2016.10.020.
@article{osti_22622255,
title = {Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model},
author = {Yang, Xiaofeng, E-mail: xfyang@math.sc.edu and Han, Daozhi, E-mail: djhan@iu.edu},
abstractNote = {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.},
doi = {10.1016/J.JCP.2016.10.020},
journal = {Journal of Computational Physics},
number = ,
volume = 330,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}