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dc.contributor.authorZheng, Xiang
dc.contributor.authorYang, Chao-he
dc.contributor.authorCai, Xiaochuan
dc.contributor.authorKeyes, David E.
dc.date.accessioned2015-08-24T08:36:39Z
dc.date.available2015-08-24T08:36:39Z
dc.date.issued2015-03
dc.identifier.citationZheng, X., Yang, C., Cai, X.-C., & Keyes, D. (2015). A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D. Journal of Computational Physics, 285, 55–70. doi:10.1016/j.jcp.2015.01.016
dc.identifier.issn00219991
dc.identifier.doi10.1016/j.jcp.2015.01.016
dc.identifier.urihttp://hdl.handle.net/10754/575726
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.
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.
dc.publisherElsevier BV
dc.subjectCahn-Hilliard-Cook
dc.subjectImplicit method
dc.subjectNewton-Krylov-Schwarz
dc.subjectParallel scalability
dc.subjectSteady state solutions
dc.subjectThermal fluctuation
dc.titleA parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentExtreme Computing Research Center
dc.identifier.journalJournal of Computational Physics
dc.contributor.institutionDepartment of Applied Physics and Applied Mathematics, Columbia UniversityNew York, NY, United States
dc.contributor.institutionInstitute of Software, Chinese Academy of SciencesBeijing, China
dc.contributor.institutionDepartment of Computer Science, University of Colorado BoulderBoulder, CO, United States
dc.contributor.institutionState Key Laboratory of Computer Science, Chinese Academy of SciencesBeijing, China
kaust.personKeyes, David E.


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