A Decoupling-Type Strategy for the Allen-Cahn Equation on Curved Surfaces  

作　　者：Xiaoman XIE Qing PAN 

机构地区：[1]School of Computer and Communication Engineering,Changsha University of Science&Technology,Hunan 410114,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2025年第1期73-83,共11页数学研究及应用(英文版)

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12171147).

摘　　要：In this paper,we construct an efficient decoupling-type strategy for solving the Allen-Cahn equation on curved surfaces.It is based on an FEM-EIEQ(Finite Element Method and explicit-Invariant Energy Quadratization)fully discrete scheme with unconditional energy stability.Spatially the FEM is adopted,using a triangular mesh discretization strategy that can be adapted to complex regions.Temporally,the EIEQ approach is considered,which not only linearizes the nonlinear potential but also gives a new variable that we combine with the nonlocal splitting method to achieve the fully decoupled computation.The strategy can successfully transform the Allen-Cahn system into some completely independent algebraic equations and linear elliptic equations with constant coefficients,we only need to solve these simple equations at each time step.Moreover,we conducted some numerical experiments to demonstrate the effectiveness of the strategy.

关 键 词：FEM-EIEQ Allen-Cahn equation SURFACE 

分 类 号：O175[理学—数学]