CONSERVATIVE MULTIGRID METHODS FOR TERNARY CAHN-HILLIARD SYSTEMS*

Junseok Kim; Kyungkeun Kang; John Lowengrub

doi:10.4310/CMS.2004.v2.n1.a4

CONSERVATIVE MULTIGRID METHODS FOR TERNARY CAHN-HILLIARD SYSTEMS*

Junseok Kim, Kyungkeun Kang, John Lowengrub

Research output: Contribution to journal › Article › peer-review

83 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 1^st 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 language	English
Pages (from-to)	53-77
Number of pages	25
Journal	Communications in Mathematical Sciences
Volume	2
Issue number	1
DOIs	https://doi.org/10.4310/CMS.2004.v2.n1.a4
Publication status	Published - 2004
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2004 International Press

Keywords

Nonlinear multigrid method
Ternary cahn-hilliard system

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4310/CMS.2004.v2.n1.a4

Cite this

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N2 - 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.

AB - 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.

KW - Nonlinear multigrid method

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JO - Communications in Mathematical Sciences

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CONSERVATIVE MULTIGRID METHODS FOR TERNARY CAHN-HILLIARD SYSTEMS*

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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