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

Journal Article · Sun Mar 15 00:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2015.01.016· OSTI ID:22465608

Zheng, Xiang ^[1]; Yang, Chao ^[2]; Cai, Xiao-Chuan ^[3]; Keyes, David ^[4]

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1. Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States)
2. Institute of Software, Chinese Academy of Sciences, Beijing 100190 (China)
3. Department of Computer Science, University of Colorado Boulder, Boulder, CO 80309 (United States)
4. Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955 (Saudi Arabia)

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.

• OSTI ID: 22465608
• Journal Information: Journal of Computational Physics, Vol. 285; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
ACCURACY
ALGORITHMS
FIELD EQUATIONS
FLUCTUATIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
STEADY-STATE CONDITIONS
STOCHASTIC PROCESSES
SUPERCOMPUTERS
THREE-DIMENSIONAL CALCULATIONS