NKS Method for the Implicit Solution of a Coupled Allen-Cahn/Cahn-Hilliard System

  • Chao Yang
  • Xiao-Chuan Cai
  • David E. Keyes
  • Michael Pernice
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 98)


The coupled Allen-Cahn/Cahn-Hilliard system consists of high-order partial differential equations that make explicit methods hard to apply due to the severe restriction on the time step size. In order to relax the restriction and obtain steady-state solution(s) in an efficient way, we use a fully implicit method for the coupled system and employ a Newton-Krylov-Schwarz algorithm to solve the nonlinear algebraic equations arising at each time step. In the Schwarz preconditioner we impose low-order homogeneous boundary conditions for subdomain problems. We investigate several choices of subdomain solvers as well as different overlaps. Numerical experiments on a supercomputer with thousands of processor cores are provided to show the scalability of the fully implicit solver.


Time Step Size Processor Core Newton Iteration Explicit Method Inexact Newton Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in part by DE-FC02-06ER25784. The first author also received supports from NSFC under 61170075, 91130023 and 61120106005, and from 973 Program of China under 2011CB309701.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Chao Yang
    • 1
    • 2
  • Xiao-Chuan Cai
    • 3
  • David E. Keyes
    • 4
  • Michael Pernice
    • 5
  1. 1.Institute of SoftwareChinese Academy of SciencesBeijingChina
  2. 2.State Key Laboratory of Computer ScienceChinese Academy of SciencesBeijingChina
  3. 3.Department of Computer ScienceUniversity of Colorado BoulderBoulderUSA
  4. 4.CEMSE DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  5. 5.Idaho National LaboratoryIdaho FallsUSA

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