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

Xiang Zheng, Chao-he Yang, Xiaochuan Cai, David E. Keyes

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)55-70
Number of pages16
JournalJournal of Computational Physics
StatePublished - Mar 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


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