Convergence Analysis of Multigrid Solver for Cahn-Hilliard Equation

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 solv...

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Bibliographic Details
Published in:Ji suan ji ke xue Vol. 50; no. 11; pp. 23 - 31
Main Authors: Guo, Jing, Qi, Deyu
Format: Journal Article
Language:Chinese
Published: Chongqing Guojia Kexue Jishu Bu 01.11.2023
Editorial office of Computer Science
Subjects:
Algorithms
Convergence
Format
Iterative methods
Nonlinear equations
nonlinear multigrid|convergence analysis|cahn-hilliard equation|full approximation scheme|nonlinear problem
Nonlinearity
Numerical methods
Parameters
Solvers
ISSN:1002-137X
Online Access:Get full text
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Summary: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
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ISSN:1002-137X
DOI:10.11896/jsjkx.220800030