Operator-based preconditioning of stiff hyperbolic systems

Daniel R. Reynolds, Ravindra Samtaney, Carol S. Woodward

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We introduce an operator-based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of PDEs posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a characteristic decomposition of the resulting directional parts. This approach allows for the solution of any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydrodynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly-evolving dynamics, scales well to large problem sizes and numbers of processors, and allows for additional customization based on the specific problems under study.

Original languageEnglish (US)
Pages (from-to)150-170
Number of pages21
JournalSIAM Journal on Scientific Computing
Volume32
Issue number1
DOIs
StatePublished - Mar 1 2010

Keywords

  • Hyperbolic systems
  • Implicit methods
  • Preconditioning

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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