Open Access
March 2004 Conservative multigrid methods for ternary Cahn-Hilliard systems
Junseok Kim, Kyungkeun Kang, John Lowengrub
Commun. Math. Sci. 2(1): 53-77 (March 2004).


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. 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.


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Junseok Kim. Kyungkeun Kang. John Lowengrub. "Conservative multigrid methods for ternary Cahn-Hilliard systems." Commun. Math. Sci. 2 (1) 53 - 77, March 2004.


Published: March 2004
First available in Project Euclid: 21 August 2009

zbMATH: 1085.65093
MathSciNet: MR2082819

Keywords: nonlinear multigrid method , Ternary Cahn-Hilliard system

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 1 • March 2004
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