Explicit Hybrid Numerical Method for the Allen-Cahn Type Equations on Curved Surfaces
- Authors
- Choi, Yongho; Li, Yibao; Lee, Chaeyoung; Kim, Hyundong; Kim, Junseok
- Issue Date
- 8월-2021
- Publisher
- GLOBAL SCIENCE PRESS
- Keywords
- Allen-Cahn equation; conservative Allen-Cahn equation; Laplace-Beltrami operator; triangular surface mesh; hybrid numerical method; PDE on surface
- Citation
- NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, v.14, no.3, pp.797 - 810
- Indexed
- SCIE
SCOPUS
- Journal Title
- NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
- Volume
- 14
- Number
- 3
- Start Page
- 797
- End Page
- 810
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/127691
- DOI
- 10.4208/nmtma.OA-2020-0155
- ISSN
- 1004-8979
- Abstract
- We present a simple and fast explicit hybrid numerical scheme for the motion by mean curvature on curved surfaces in three-dimensional (3D) space. We numerically solve the Allen-Cahn (AC) and conservative Allen-Cahn (CAC) equations on a triangular surface mesh. We use the operator splitting method and an explicit hybrid numerical method. For the AC equation, we solve the diffusion term using a discrete Laplace-Beltrami operator on the triangular surface mesh and solve the reaction term using the closed-form solution, which is obtained using the separation of variables. Next, for the CAC equation, we additionally solve the time-space dependent Lagrange multiplier using an explicit scheme. Our numerical scheme is computationally fast and efficient because we use an explicit hybrid numerical scheme. We perform various numerical experiments to demonstrate the robustness and efficiency of the proposed scheme.
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Collections - College of Science > Department of Mathematics > 1. Journal Articles
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