Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces
This paper describes temporally second-order unconditionally stable direct methods for Allen–Cahn and conservative Allen–Cahn equations on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. We prove that the pro...
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doaj-2897077d65344c749debd0e80d4890522020-11-25T03:27:11ZengMDPI AGMathematics2227-73902020-09-0181486148610.3390/math8091486Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on SurfacesBinhu Xia0Yibao Li1Zhong Li2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Humanities and Social Science, Xi’an Jiaotong University, Xi’an 710049, ChinaThis paper describes temporally second-order unconditionally stable direct methods for Allen–Cahn and conservative Allen–Cahn equations on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. We prove that the proposed schemes, which combine a linearly stabilized splitting scheme, are unconditionally energy-stable. The resulting system of discrete equations is linear and is simple to implement. Several numerical experiments are performed to demonstrate the performance of our proposed algorithm.https://www.mdpi.com/2227-7390/8/9/1486Allen–Cahn equationconservative Allen–Cahn equationLaplace–Beltrami operatortriangular surface meshunconditionally energy-stable |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Binhu Xia Yibao Li Zhong Li |
spellingShingle |
Binhu Xia Yibao Li Zhong Li Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces Mathematics Allen–Cahn equation conservative Allen–Cahn equation Laplace–Beltrami operator triangular surface mesh unconditionally energy-stable |
author_facet |
Binhu Xia Yibao Li Zhong Li |
author_sort |
Binhu Xia |
title |
Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces |
title_short |
Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces |
title_full |
Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces |
title_fullStr |
Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces |
title_full_unstemmed |
Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces |
title_sort |
second-order unconditionally stable direct methods for allen–cahn and conservative allen–cahn equations on surfaces |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2020-09-01 |
description |
This paper describes temporally second-order unconditionally stable direct methods for Allen–Cahn and conservative Allen–Cahn equations on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. We prove that the proposed schemes, which combine a linearly stabilized splitting scheme, are unconditionally energy-stable. The resulting system of discrete equations is linear and is simple to implement. Several numerical experiments are performed to demonstrate the performance of our proposed algorithm. |
topic |
Allen–Cahn equation conservative Allen–Cahn equation Laplace–Beltrami operator triangular surface mesh unconditionally energy-stable |
url |
https://www.mdpi.com/2227-7390/8/9/1486 |
work_keys_str_mv |
AT binhuxia secondorderunconditionallystabledirectmethodsforallencahnandconservativeallencahnequationsonsurfaces AT yibaoli secondorderunconditionallystabledirectmethodsforallencahnandconservativeallencahnequationsonsurfaces AT zhongli secondorderunconditionallystabledirectmethodsforallencahnandconservativeallencahnequationsonsurfaces |
_version_ |
1724589016208113664 |