Convergence Analysis of Multigrid Solver for Cahn-Hilliard Equation - Guo, Jing; Qi, Deyu (Ji suan ji ke xue, 2023)
The Cahn-Hilliard（CH） equation is a fundamental nonlinear equation in the phase field model and is usually analyzed using numerical methods.Following a numerical discretization, we get a nonlinear equations system.The full approximation scheme（FAS） is an efficient multigrid iterative scheme for solving such nonlinear equations.In the numerous articles on solving the CH equation, the main focus is on the convergence of the numerical format, without mentioning the stability of the solver.In this paper, the convergence property of the multigrid algorithm is established, which is from the nonlinear equation system obtained by solving the discrete CH equation, and the reliability of the calculation process is guaranteed theoretically.For the diffe-rence discrete numerical scheme of the CH equation, which is both second-order in spatial and time, we use the fast subspace descent method（FASD） framework to give the estimation of the convergence constant of its FAS scheme multigrid solver.First, we transform the origi