Nonlinear multigrid implementation for the two-dimensional cahn-hilliard equation

Chaeyoung Lee, Darae Jeong, Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We present a nonlinear multigrid implementation for the two-dimensional Cahn-Hilliard (CH) equation and conduct detailed numerical tests to explore the performance of the multigrid method for the CH equation. The CH equation was originally developed by Cahn and Hilliard to model phase separation phenomena. The CH equation has been used to model many interface-related problems, such as the spinodal decomposition of a binary alloy mixture, inpainting of binary images, microphase separation of diblock copolymers, microstructures with elastic inhomogeneity, two-phase binary fluids, in silico tumor growth simulation and structural topology optimization. The CH equation is discretized by using Eyre's unconditionally gradient stable scheme. The system of discrete equations is solved using an iterative method such as a nonlinear multigrid approach, which is one of the most efficient iterative methods for solving partial differential equations. Characteristic numerical experiments are conducted to demonstrate the efficiency and accuracy of the multigrid method for the CH equation. In the Appendix, we provide C code for implementing the nonlinear multigrid method for the two-dimensional CH equation.

Original languageEnglish
Article number97
Issue number1
Publication statusPublished - 2020 Jan 1


  • Cahn-Hilliard equation
  • multigrid method
  • unconditionally gradient stable scheme

ASJC Scopus subject areas

  • Mathematics(all)


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