ENERGY DIMINISHING IMPLICIT-EXPLICIT RUNGE-KUTTA METHODS FOR GRADIENT FLOWS

Fu, Zhaohui1; Tang, Tao2,3; Yang, Jiang4,5

2024-02-01

10.1090/mcom/3950

MATHEMATICS OF COMPUTATION   影响因子和分区

0025-5718

1088-6842

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.

IMEX Runge-Kutta gradient flows energy stability phase field equations

SCI

英语

通讯

National Science Foundation of China[NSFC-12271240] ; Hong Kong RGC Joint Research Scheme[NSFC/RGC 11961160718] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001] ; Shenzhen Natural Science Fund[RCJC20210609103819018] ; Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science[UIC 2022B1212010006]

Mathematics

Mathematics, Applied

WOS:001176966000001

AMER MATHEMATICAL SOC

MATHEMATICS

Web of Science

1.Univ British Columbia, Dept Math, Vancouver, BC, Canada
2.BNU HKBU United Int Coll, Zhuhai 519087, Peoples R China
3.Guangdong Prov Key Lab Interdisciplinary Res & App, Shenzhen, Peoples R China
4.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Dept Math, Shenzhen 518055, Peoples R China
5.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen NCAMS, Shenzhen 518055, Peoples R China

Fu, Zhaohui,Tang, Tao,Yang, Jiang. ENERGY DIMINISHING IMPLICIT-EXPLICIT RUNGE-KUTTA METHODS FOR GRADIENT FLOWS[J]. MATHEMATICS OF COMPUTATION,2024.

Fu, Zhaohui,Tang, Tao,&Yang, Jiang.(2024).ENERGY DIMINISHING IMPLICIT-EXPLICIT RUNGE-KUTTA METHODS FOR GRADIENT FLOWS.MATHEMATICS OF COMPUTATION.

Fu, Zhaohui,et al."ENERGY DIMINISHING IMPLICIT-EXPLICIT RUNGE-KUTTA METHODS FOR GRADIENT FLOWS".MATHEMATICS OF COMPUTATION (2024).