A multigrid solution for the Cahn–Hilliard equation on nonuniform grids

Yongho Choi, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We present a nonlinear multigrid method to solve the Cahn–Hilliard (CH) equation on nonuniform grids. The CH equation was originally proposed as a mathematical model to describe phase separation phenomena after the quenching of binary alloys. The model has the characteristics of thin diffusive interfaces. To resolve the sharp interfacial transition, we need a very fine grid, which is computationally expensive. To reduce the cost, we can use a fine grid around the interfacial transition region and a relatively coarser grid in the bulk region. The CH equation is discretized by a conservative finite difference scheme in space and an unconditionally gradient stable type scheme in time. We use a conservative restriction in the nonlinear multigrid method to conserve the total mass in the coarser grid levels. Various numerical results on one-, two-, and three-dimensional spaces are presented to demonstrate the accuracy and effectiveness of the nonuniform grids for the CH equation.

Original languageEnglish
Pages (from-to)320-333
Number of pages14
JournalApplied Mathematics and Computation
Publication statusPublished - 2017 Jan 15

Bibliographical note

Funding Information:
The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper.

Publisher Copyright:
© 2016 Elsevier Inc.

Copyright 2017 Elsevier B.V., All rights reserved.


  • Cahn–Hilliard equation
  • Finite difference method
  • Multigrid method
  • Nonuniform grid

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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