A structure-preserving and variable-step BDF2 Fourier pseudo-spectral method for the two-mode phase field crystal model

被引：6

作者：

Li, Dongfang ^{[1
,2
]}

Li, Xiaoxi ^{[1
]}

Mei, Ming ^{[3
,4
]}

Yuan, Wanqiu ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

[3] Champlain Coll St Lambert, Dept Math, St Lambert, PQ J4P 3P2, Canada

[4] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2023年 / 205卷

基金：

中国国家自然科学基金;

关键词：

Variable-step BDF2 scheme; Two-mode phase-field crystal model; Robust L2 error estimate; Structure-preserving; FINITE-DIFFERENCE SCHEME; ENERGY STABLE SCHEMES; NUMERICAL SCHEME; CONVERGENCE ANALYSIS; 2ND-ORDER; CAHN; STABILITY; EQUATION;

D O I：

10.1016/j.matcom.2022.10.009

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

For the two-mode phase field crystal models, the evolutions of the solutions and energy vary fast at certain time. To resolve varying time scales efficiently and reduce the computational cost, a variable-step BDF2 Fourier pseudo-spectral method is proposed. It is shown that the fully-discrete scheme is volume-conserving and unconditional energy-stable. Moreover, a robust error estimate is established by using the discrete orthogonal convolution kernels and the corresponding convolution inequalities. Numerical experiments by using the random and adaptive time-stepping strategies are presented to confirm the effectiveness of the scheme. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：483 / 506

页数：24

共 14 条

[1] An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation
Cheng, Kelong
Wang, Cheng
Wise, Steven M.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2019, 26 (05) : 1335 - 1364
[2] A variable-step, structure-preserving and linear fully discrete scheme for the two-mode phase-field crystal model with face-centered-cubic ordering
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[3] Errors of an Implicit Variable-Step BDF2 Method for a Molecular Beam Epitaxial Model with Slope Selection
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[4] Asymptotically compatible energy of two variable-step fractional BDF2 schemes for the time fractional Allen-Cahn model
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[5] Structure-preserving weighted BDF2 methods for anisotropic Cahn-Hilliard model: Uniform/variable-time-steps
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[6] An adaptive BDF2 implicit time-stepping method for the phase field crystal model
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IMA JOURNAL OF NUMERICAL ANALYSIS, 2022, 42 (01) : 649 - 679
[7] An efficient two-grid high-order compact difference scheme with variable-step BDF2 method for the semilinear parabolic equation
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Fu, Hongfei
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[8] Sharp Error Estimate of an Implicit BDF2 Scheme with Variable Time Steps for the Phase Field Crystal Model
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Yifan Wei
Jiwei Zhang
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[9] Sharp Error Estimate of an Implicit BDF2 Scheme with Variable Time Steps for the Phase Field Crystal Model
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Wei, Yifan
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JOURNAL OF SCIENTIFIC COMPUTING, 2022, 92 (02)
[10] Energy dissipation and evolutions of the nonlocal Cahn-Hilliard model and space fractional variants using efficient variable-step BDF2 method
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Zhai, Shuying
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JOURNAL OF COMPUTATIONAL PHYSICS, 2024, 510

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