Preconditioning waveform relaxation iterations for differential systems

K. Burrage, Zdzislaw Jackiewicz, S. P. Nørsett, Rosemary Renaut

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We discuss preconditioning and overlapping of waveform relaxation methods for sparse linear differential systems. It is demonstrated that these techniques significantly improve the speed of convergence of the waveform relaxation iterations resulting from application of various modes of block Gauss-Jacobi and block Gauss-Seidel methods to differential systems. Numerical results are presented for linear systems resulting from semi-discretization of the heat equation in one and two space variables. It turns out that overlapping is very effective for the system corresponding to the one-dimensional heat equation and preconditioning is very effective for the system corresponding to the two-dimensional case.

Original languageEnglish (US)
Pages (from-to)54-76
Number of pages23
JournalBIT Numerical Mathematics
Volume36
Issue number1
DOIs
StatePublished - Mar 1996

Keywords

  • Error analysis
  • Overlapping
  • Parallel computing
  • Preconditioning
  • Splittings
  • Waveform relaxation

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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