First- and second-order energy stable methods for the modified phase field crystal equation

被引：40

作者：

Lee, Hyun Geun ^{[1
]}

Shin, Jaemin ^{[2
]}

Lee, June-Yub ^{[3
]}

机构：

[1] Kwangwoon Univ, Dept Math, Seoul 01897, South Korea

[2] Ewha Womans Univ, Inst Math Sci, Seoul 03760, South Korea

[3] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2017年 / 321卷

基金：

新加坡国家研究基金会;

关键词：

Phase field crystal equation; Modified phase field crystal equation; Energy stability; Fourier spectral method; FINITE-DIFFERENCE SCHEME; MODELS;

D O I：

10.1016/j.cma.2017.03.033

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The phase field crystal (PFC) model was extended to the modified phase field crystal (MPFC) model, which is a sixth-order nonlinear damped wave equation, to include not only diffusive dynamics but also elastic interactions. In this paper, we present temporally first- and second-order accurate methods for the MPFC equation, which are based on an appropriate splitting of the energy for the PFC equation. And we use the Fourier spectral method for the spatial discretization. The first- and second-order methods are shown analytically to be unconditionally stable with respect to the energy and pseudoenergy of the MPFC equation, respectively. Numerical experiments are presented demonstrating the accuracy and energy stability of the proposed methods. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：1 / 17

页数：17

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