A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D

Handle URI:
http://hdl.handle.net/10754/575726
Title:
A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D
Authors:
Zheng, Xiang; Yang, Chao; Cai, Xiaochuan; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors. © 2015 Elsevier Inc.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Extreme Computing Research Center
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Mar-2015
DOI:
10.1016/j.jcp.2015.01.016
Type:
Article
ISSN:
00219991
Sponsors:
The authors wish to thank Professor Marc Spiegelman and Professor Yuefan Deng for many helpful discussions. This work was supported by the U.S. Department of Energy (under Contract No. DE-FC02-06ER25784). Their support is gratefully acknowledged.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorZheng, Xiangen
dc.contributor.authorYang, Chaoen
dc.contributor.authorCai, Xiaochuanen
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2015-08-24T08:36:39Zen
dc.date.available2015-08-24T08:36:39Zen
dc.date.issued2015-03en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2015.01.016en
dc.identifier.urihttp://hdl.handle.net/10754/575726en
dc.description.abstractWe present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors. © 2015 Elsevier Inc.en
dc.description.sponsorshipThe authors wish to thank Professor Marc Spiegelman and Professor Yuefan Deng for many helpful discussions. This work was supported by the U.S. Department of Energy (under Contract No. DE-FC02-06ER25784). Their support is gratefully acknowledged.en
dc.publisherElsevier BVen
dc.subjectCahn-Hilliard-Cooken
dc.subjectImplicit methoden
dc.subjectNewton-Krylov-Schwarzen
dc.subjectParallel scalabilityen
dc.subjectSteady state solutionsen
dc.subjectThermal fluctuationen
dc.titleA parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3Den
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionDepartment of Applied Physics and Applied Mathematics, Columbia UniversityNew York, NY, United Statesen
dc.contributor.institutionInstitute of Software, Chinese Academy of SciencesBeijing, Chinaen
dc.contributor.institutionDepartment of Computer Science, University of Colorado BoulderBoulder, CO, United Statesen
dc.contributor.institutionState Key Laboratory of Computer Science, Chinese Academy of SciencesBeijing, Chinaen
kaust.authorKeyes, David E.en
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