Stabilized explicit-implicit domain decomposition methods for the numerical solution of parabolic equations

Yu Zhuang, Xian He Sun

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

Abstract

We report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the numerical solution of parabolic equations. Explicit-implicit domain decomposition (EIDD) methods are globally noniterative, nonoverlapping domain decomposition methods, which, when compared with Schwarz-algorithm-based parabolic solvers, are computationally and communicationally efficient for each simulation time step but suffer from small time step size restrictions. By adding a stabilization step to EIDD, the SEIDD methods retain the time-stepwise efficiency in computation and communication of the EIDD methods but exhibit much better numerical stability. Three SEIDD algorithms are presented in this paper, which are experimentally tested to show excellent stability, computation and communication efficiencies, and high parallel speedup and scalability.

Original languageEnglish
Pages (from-to)335-358
Number of pages24
JournalSIAM Journal on Scientific Computing
Volume24
Issue number1
DOIs
StatePublished - 2003

Keywords

  • Globally noniterative method
  • Nonoverlapping domain decomposition
  • Parabolic equation
  • Parallel computing

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