A parallel multigrid method of the Cahn-Hilliard equation

Jaemin Shin; Sungki Kim; Dongsun Lee; Junseok Kim

doi:10.1016/j.commatsci.2013.01.008

A parallel multigrid method of the Cahn-Hilliard equation

Jaemin Shin, Sungki Kim, Dongsun Lee, Junseok Kim

Department of Mathematics

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

16 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 language	English
Pages (from-to)	89-96
Number of pages	8
Journal	Computational Materials Science
Volume	71
DOIs	https://doi.org/10.1016/j.commatsci.2013.01.008
Publication status	Published - 2013

Keywords

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

ASJC Scopus subject areas

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

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10.1016/j.commatsci.2013.01.008

Cite this

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title = "A parallel multigrid method of the Cahn-Hilliard equation",

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.",

keywords = "Cahn-Hilliard equation, Linearly stabilized splitting scheme, Multigrid, Parallel computing, Phase separation",

author = "Jaemin Shin and Sungki Kim and Dongsun Lee and Junseok Kim",

note = "Funding Information: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-0023794). The simulations were performed using the GAIA supercomputing cluster at the KISTI Supercomputing Center. The authors thank the reviewers for their useful and constructive comments on this article.",

year = "2013",

doi = "10.1016/j.commatsci.2013.01.008",

language = "English",

volume = "71",

pages = "89--96",

journal = "Computational Materials Science",

issn = "0927-0256",

publisher = "Elsevier",

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TY - JOUR

T1 - A parallel multigrid method of the Cahn-Hilliard equation

AU - Shin, Jaemin

AU - Kim, Sungki

AU - Lee, Dongsun

AU - Kim, Junseok

N1 - Funding Information: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2011-0023794). The simulations were performed using the GAIA supercomputing cluster at the KISTI Supercomputing Center. The authors thank the reviewers for their useful and constructive comments on this article.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Cahn-Hilliard equation

KW - Linearly stabilized splitting scheme

KW - Multigrid

KW - Parallel computing

KW - Phase separation

UR - http://www.scopus.com/inward/record.url?scp=84873962115&partnerID=8YFLogxK

U2 - 10.1016/j.commatsci.2013.01.008

DO - 10.1016/j.commatsci.2013.01.008

M3 - Article

AN - SCOPUS:84873962115

SN - 0927-0256

VL - 71

SP - 89

EP - 96

JO - Computational Materials Science

JF - Computational Materials Science

ER -

A parallel multigrid method of the Cahn-Hilliard equation

Abstract

Keywords

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