发表状态 | 已发表Published |
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
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ISSN/eISSN | 0025-5718 |
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 |
DOI | 10.1090/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 | |
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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