Year: 2021
Author: Junseok Kim, Yongho Choi, Yibao Li, Chaeyoung Lee, Hyundong Kim, Junseok Kim
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 797–810
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0155
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 797–810
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Allen-Cahn equation conservative Allen-Cahn equation Laplace-Beltrami operator triangular surface mesh hybrid numerical method PDE on surface.
Author Details
-
Fast and efficient numerical method for solving the Allen–Cahn equation on the cubic surface
Hwang, Youngjin | Yang, Junxiang | Lee, Gyeongyu | Ham, Seokjun | Kang, Seungyoon | Kwak, Soobin | Kim, JunseokMathematics and Computers in Simulation, Vol. 215 (2024), Iss. P.338
https://doi.org/10.1016/j.matcom.2023.07.024 [Citations: 1] -
Shape transformation on curved surfaces using a phase-field model
Kim, Hyundong | Kang, Seungyoon | Lee, Gyeonggyu | Yoon, Sungha | Kim, JunseokCommunications in Nonlinear Science and Numerical Simulation, Vol. 133 (2024), Iss. P.107956
https://doi.org/10.1016/j.cnsns.2024.107956 [Citations: 3] -
A simple and efficient numerical method for the Allen–Cahn equation on effective symmetric triangular meshes
Hwang, Youngjin | Ham, Seokjun | Lee, Chaeyoung | Lee, Gyeonggyu | Kang, Seungyoon | Kim, JunseokElectronic Research Archive, Vol. 31 (2023), Iss. 8 P.4557
https://doi.org/10.3934/era.2023233 [Citations: 2]