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题名ENERGY DIMINISHING IMPLICIT-EXPLICIT RUNGE–KUTTA METHODS FOR GRADIENT FLOWS
作者
发表日期2024-11-01
发表期刊Mathematics of Computation
ISSN/eISSN0025-5718
卷号93期号:350页码:2745-2767
摘要

This study focuses on the development and analysis of a group of high-order implicit-explicit (IMEX) Runge–Kutta (RK) methods that are suitable for discretizing gradient flows with nonlinearity that is Lipschitz continuous. We demonstrate that these IMEX-RK methods can preserve the original energy dissipation property without any restrictions on the time-step size, thanks to a stabilization technique. The stabilization constants are solely dependent on the minimal eigenvalues that result from the Butcher tables of the IMEX-RKs. Furthermore, we establish a simple framework that can determine whether an IMEX-RK scheme is capable of preserving the original energy dissipation property or not. We also present a heuristic convergence analysis based on the truncation errors. This is the first research to prove that a linear high-order single-step scheme can ensure the original energy stability unconditionally for general gradient flows. Additionally, we provide several high-order IMEX-RK schemes that satisfy the established framework. Notably, we discovered a new four-stage third-order IMEX-RK scheme that reduces energy. Finally, we provide numerical examples to demonstrate the stability and accuracy properties of the proposed methods.

关键词energy stability gradient flows IMEX Runge–Kutta phase field equations
DOI10.1090/mcom/3950
URL查看来源
收录类别SCIE
语种英语English
WOS研究方向Mathematics
WOS类目Mathematics, Applied
WOS记录号WOS:001176966000001
Scopus入藏号2-s2.0-85194337478
引用统计
被引频次:16[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符https://repository.uic.edu.cn/handle/39GCC9TT/11959
专题理工科技学院
作者单位
1.Department of Mathematics,University of British Columbia,Vancouver,Canada
2.BNU-HKBU United International College,Zhuhai,519087,China
3.Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,China
4.Department of Mathematics,SUSTech International Center for Mathematics & National Center for Applied Mathematics Shenzhen (NCAMS),Southern University of Science and Technology,Shenzhen,518055,China
推荐引用方式
GB/T 7714
Fu, Zhaohui,Tang, Tao,Yang, Jiang. ENERGY DIMINISHING IMPLICIT-EXPLICIT RUNGE–KUTTA METHODS FOR GRADIENT FLOWS[J]. Mathematics of Computation, 2024, 93(350): 2745-2767.
APA Fu, Zhaohui, Tang, Tao, & Yang, Jiang. (2024). ENERGY DIMINISHING IMPLICIT-EXPLICIT RUNGE–KUTTA METHODS FOR GRADIENT FLOWS. Mathematics of Computation, 93(350), 2745-2767.
MLA Fu, Zhaohui,et al."ENERGY DIMINISHING IMPLICIT-EXPLICIT RUNGE–KUTTA METHODS FOR GRADIENT FLOWS". Mathematics of Computation 93.350(2024): 2745-2767.
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