南方科技大学知识苑(SUSTech KC): Energy Plus Maximum Bound Preserving Runge-Kutta Methods for the Allen-Cahn Equation

题名	Energy Plus Maximum Bound Preserving Runge-Kutta Methods for the Allen-Cahn Equation
作者	Fu, Zhaohui1,2 ; Tang, Tao3,4,5 ; Yang, Jiang1,4,5
通讯作者	Yang, Jiang
发表日期	2022-09-01
DOI	10.1007/s10915-022-01940-6
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING 影响因子和分区
ISSN	0885-7474
EISSN	1573-7691
卷号	92 期号:3
摘要	It is difficult to design high order numerical schemes which could preserve both the maximum bound property (MBP) and energy dissipation law for certain phase field equations. Strong stability preserving (SSP) Runge-Kutta methods have been developed for numerical solution of hyperbolic partial differential equations in the past few decades, where strong stability means the non-increasing of the maximum bound of the underlying solutions. However, existing framework of SSP RK methods can not handle nonlinear stabilities like energy dissipation law. The aim of this work is to extend this SSP theory to deal with the nonlinear phase field equation of the Allen-Cahn type which typically satisfies both maximum bound preserving (MBP) and energy dissipation law. More precisely, for Runge-Kutta time discretizations, we first derive a general necessary and sufficient condition under which MBP is satisfied; and we further provide a necessary condition under which the MBP scheme satisfies energy dissipation.
关键词	Allen-Cahn equation Maximum principle Energy dissipation law Runge-Kutta methods
相关链接	[来源记录]
收录类别	SCI ; EI
语种	英语
学校署名	第一 ; 通讯
资助项目	National Natural Science Foundation of China (NSFC)[11871264] ; Natural Science Foundation of Guangdong Province[2018A0303130123] ; Shenzhen Natural Science Fund[RCJC20210609103819018] ; NSFC/Hong Kong RRC Joint Research Scheme[NFSC/RGC 11961160718]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000834864600008
出版者	SPRINGER/PLENUM PUBLISHERS
EI入藏号	20223112525883
EI主题词	Maximum principle ; Nonlinear equations ; Numerical methods ; Runge Kutta methods
EI分类号	Energy Losses (industrial and residential):525.4 ; Numerical Methods:921.6
ESI学科分类	MATHEMATICS
来源库	Web of Science
引用统计	被引频次[WOS]：7
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/375564
专题	理学院_数学系
作者单位	1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China 2.Univ British Columbia, Dept Math, Vancouver, BC, Canada 3.BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai 519000, Peoples R China 4.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen, Peoples R China 5.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen NCAMS, Shenzhen, Peoples R China
第一作者单位	数学系
通讯作者单位	数学系; 南方科技大学
第一作者的第一单位	数学系
推荐引用方式 GB/T 7714	Fu, Zhaohui,Tang, Tao,Yang, Jiang. Energy Plus Maximum Bound Preserving Runge-Kutta Methods for the Allen-Cahn Equation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2022,92(3).
APA	Fu, Zhaohui,Tang, Tao,&Yang, Jiang.(2022).Energy Plus Maximum Bound Preserving Runge-Kutta Methods for the Allen-Cahn Equation.JOURNAL OF SCIENTIFIC COMPUTING,92(3).
MLA	Fu, Zhaohui,et al."Energy Plus Maximum Bound Preserving Runge-Kutta Methods for the Allen-Cahn Equation".JOURNAL OF SCIENTIFIC COMPUTING 92.3(2022).