| Title | Energy Plus Maximum Bound Preserving Runge-Kutta Methods for the Allen-Cahn Equation |
| Author | |
| Corresponding Author | Yang, Jiang |
| Publication Years | 2022-09-01
|
| DOI | |
| Source Title | |
| ISSN | 0885-7474
|
| EISSN | 1573-7691
|
| Volume | 92Issue:3 |
| Abstract | 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. |
| Keywords | |
| URL | [Source Record] |
| Indexed By | |
| Language | English
|
| SUSTech Authorship | First
; Corresponding
|
| Funding Project | 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 Research Area | Mathematics
|
| WOS Subject | Mathematics, Applied
|
| WOS Accession No | WOS:000834864600008
|
| Publisher | |
| EI Accession Number | 20223112525883
|
| EI Keywords | Maximum principle
; Nonlinear equations
; Numerical methods
; Runge Kutta methods
|
| ESI Classification Code | Energy Losses (industrial and residential):525.4
; Numerical Methods:921.6
|
| ESI Research Field | MATHEMATICS
|
| Data Source | Web of Science
|
| Citation statistics |
Cited Times [WOS]:0
|
| Document Type | Journal Article |
| Identifier | http://kc.sustech.edu.cn/handle/2SGJ60CL/375564 |
| Department | Department of Mathematics |
| Affiliation | 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 |
| First Author Affilication | Department of Mathematics |
| Corresponding Author Affilication | Department of Mathematics; Southern University of Science and Technology; |
| First Author's First Affilication | Department of Mathematics |
| Recommended Citation 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).
|
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