A parallel multigrid method of the Cahn-Hilliard equation

Jaemin Shin, Sungki Kim, Dongsun Lee, Junseok Kim

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We present a parallel finite difference scheme and its implementation for solving the Cahn-Hilliard equation, which describes the phase separation process. Our numerical algorithm employs an unconditionally gradient stable splitting discretization method. The resulting discrete equations are solved using a parallel multigrid method. This parallel scheme facilitates the solution of large-scale problems. We provide numerical results related to the speed-up, efficiency, and scalability to demonstrate the high performance of our proposed method. We also propose a linearly stabilized splitting scheme for the Cahn-Hilliard equation with logarithmic free energy.

Original languageEnglish
Pages (from-to)89-96
Number of pages8
JournalComputational Materials Science
Volume71
DOIs
Publication statusPublished - 2013 Feb 21

Fingerprint

multigrid methods
Cahn-Hilliard Equation
Parallel Methods
Multigrid Method
Phase separation
Free energy
Scalability
Discretization Method
Splitting Method
Phase Separation
Large-scale Problems
Discrete Equations
Finite Difference Scheme
Numerical Algorithms
Free Energy
Logarithmic
Speedup
High Performance
Linearly
Gradient

Keywords

  • Cahn-Hilliard equation
  • Linearly stabilized splitting scheme
  • Multigrid
  • Parallel computing
  • Phase separation

ASJC Scopus subject areas

  • Materials Science(all)
  • Chemistry(all)
  • Computer Science(all)
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Mechanics of Materials

Cite this

A parallel multigrid method of the Cahn-Hilliard equation. / Shin, Jaemin; Kim, Sungki; Lee, Dongsun; Kim, Junseok.

In: Computational Materials Science, Vol. 71, 21.02.2013, p. 89-96.

Research output: Contribution to journalArticle

Shin, Jaemin ; Kim, Sungki ; Lee, Dongsun ; Kim, Junseok. / A parallel multigrid method of the Cahn-Hilliard equation. In: Computational Materials Science. 2013 ; Vol. 71. pp. 89-96.
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