CONSERVATIVE MULTIGRID METHODS FOR TERNARY CAHN-HILLIARD SYSTEMS*

Junseok Kim, Kyungkeun Kang, John Lowengrub

Research output: Contribution to journalArticlepeer-review

75 Citations (Scopus)

Abstract

We develop a conservative, second order accurate fully implicit discretization of ternary (three-phase) Cahn-Hilliard (CH) systems that has an associated discrete energy functional. This is an extension of our work for two-phase systems [13]. We analyze and prove convergence of the scheme. To efficiently solve the discrete system at the implicit time-level, we use a nonlinear multigrid method. The resulting scheme is efficient, robust and there is at most a 1st order time step constraint for stability. We demonstrate convergence of our scheme numerically and we present several simulations of phase transitions in ternary systems.

Original languageEnglish
Pages (from-to)53-77
Number of pages25
JournalCommunications in Mathematical Sciences
Volume2
Issue number1
DOIs
Publication statusPublished - 2004
Externally publishedYes

Keywords

  • Nonlinear multigrid method
  • Ternary cahn-hilliard system

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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