@Article{NMTMA-14-3,
author = {Kim, Junseok and Yongho, Choi and Yibao, Li and Lee, Chaeyoung and Kim, Hyundong and Kim, Junseok},
title = {Explicit Hybrid Numerical Method for the Allen-Cahn Type Equations on Curved Surfaces},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2021},
volume = {14},
number = {3},
pages = {797--810},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2020-0155},
url = {https://global-sci.com/article/90320/explicit-hybrid-numerical-method-for-the-allen-cahn-type-equations-on-curved-surfaces}
}