| Novel energy dissipative method on the adaptive spatial discretization for the Allen–Cahn equation |
| |
| 作者单位： | 1.Department of Mathematics, National University of Defense Technology, Changsha 410073, China;2.State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China |
| |
| 摘 要： | We propose a novel energy dissipative method for the Allen–Cahn equation on nonuniform grids. For spatial discretization, the classical central difference method is utilized, while the average vector field method is applied for time discretization. Compared with the average vector field method on the uniform mesh, the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation. This is due to the moving mesh method, which can concentrate the grid points more densely where the solution changes drastically. Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time.
|
| 收稿时间： | 2020-12-25 |
Novel energy dissipative method on the adaptive spatial discretization for the Allen-Cahn equation |
| |
| Affiliation: | 1.Department of Mathematics, National University of Defense Technology, Changsha 410073, China;2.State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China |
| |
| Abstract: | We propose a novel energy dissipative method for the Allen-Cahn equation on nonuniform grids. For spatial discretization, the classical central difference method is utilized, while the average vector field method is applied for time discretization. Compared with the average vector field method on the uniform mesh, the proposed method can involve fewer grid points and achieve better numerical performance over long time simulation. This is due to the moving mesh method, which can concentrate the grid points more densely where the solution changes drastically. Numerical experiments are provided to illustrate the advantages of the proposed concrete adaptive energy dissipative scheme under large time and space steps over a long time. |
| |
| Keywords: | moving mesh energy dissipative average vector field method Allen-Cahn equation |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《中国物理 B》浏览原始摘要信息 |
|
点击此处可从《中国物理 B》下载免费的PDF全文 |
|
