A decoupling-type strategy for the Allen–Cahn equation on curved surfaces
Received:January 04, 2024  Revised:February 27, 2024
Key Words: FEM-EIEQ   decoupled   Allen–Cahn equation  
Fund Project:
Author NameAffiliationAddress
Xiaoman XIE* Changsha University of Science and Technology Jinpenling Campus, Changsha University of Science and Technology, Tianxin District, Changsha, Hunan Province, China
Qing PAN Changsha University of Science and Technology Jinpenling Campus, Changsha University of Science and Technology, Tianxin District, Changsha, Hunan Province, China
Hits: 72
Download times: 0
Abstract:
      In this study, we construct an efficient decoupling-type strategy for solving the Allen-Cahn equation on curved surfaces. It is based on a 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.
Citation:
DOI:
  View/Add Comment