A parallel multigrid method of the Cahn–Hilliard equation

► We present the parallel multigrid algorithm for solving the Cahn–Hilliard equation. ► We show parallel performances containing the speed-up, efficiency, and scalability. ► We propose a linearly stabilized splitting scheme for a logarithmic free energy. We present a parallel finite difference schem...

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Published in:Computational materials science Vol. 71; pp. 89 - 96
Main Authors: Shin, Jaemin, Kim, Sungki, Lee, Dongsun, Kim, Junseok
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.04.2013
Elsevier
Subjects:
Cahn–Hilliard equation
Condensed matter: structure, mechanical and thermal properties
Equations of state, phase equilibria, and phase transitions
Exact sciences and technology
Linearly stabilized splitting scheme
Multigrid
Parallel computing
Phase separation
Physics
Solubility, segregation, and mixing; phase separation
Linearly stabilized splitting scheme
Parallel computing
Multigrid
Phase separation
Cahn–Hilliard equation
High performance
Cahn-Hilliard equation
Spinodal decomposition
Free energy
Discretization method
Grain coarsening
Cahn Hilliard equation
Displacement rates
Parallel computation
Finite difference method
ISSN:0927-0256, 1879-0801
Online Access:Get full text
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Abstract ► We present the parallel multigrid algorithm for solving the Cahn–Hilliard equation. ► We show parallel performances containing the speed-up, efficiency, and scalability. ► We propose a linearly stabilized splitting scheme for a logarithmic free energy. 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.
AbstractList ► We present the parallel multigrid algorithm for solving the Cahn–Hilliard equation. ► We show parallel performances containing the speed-up, efficiency, and scalability. ► We propose a linearly stabilized splitting scheme for a logarithmic free energy. 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.
Author Kim, Junseok
Kim, Sungki
Shin, Jaemin
Lee, Dongsun
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Keywords Linearly stabilized splitting scheme
Parallel computing
Multigrid
Phase separation
Cahn–Hilliard equation
High performance
Cahn-Hilliard equation
Spinodal decomposition
Free energy
Discretization method
Grain coarsening
Cahn Hilliard equation
Displacement rates
Parallel computation
Finite difference method
Language English
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Snippet ► We present the parallel multigrid algorithm for solving the Cahn–Hilliard equation. ► We show parallel performances containing the speed-up, efficiency, and...
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SubjectTerms Cahn–Hilliard equation
Condensed matter: structure, mechanical and thermal properties
Equations of state, phase equilibria, and phase transitions
Exact sciences and technology
Linearly stabilized splitting scheme
Multigrid
Parallel computing
Phase separation
Physics
Solubility, segregation, and mixing; phase separation
Title A parallel multigrid method of the Cahn–Hilliard equation
URI https://dx.doi.org/10.1016/j.commatsci.2013.01.008
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