A parallel Schwarz method for a convection-diffusion problem

M. Garbey, Y. A. Kuznetsov, Y. V. Vassilevski

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


This paper describes a parallel convection-diffusion solver which may be used as part of a Navier-Stokes solver for three-dimensional channel flow at moderately large Reynolds numbers [S. Turek, Efficient Solvers for Incompessible Flow Problems: An Algorithmic Approach in View of Computational Aspects, Springer-Verlag, 1999]. The solver uses a multiplicative Schwarz domain decomposition with overlapping subdomains to solve singularly perturbed convection-diffusion equations where convection is dominant. Upwind finite differences are used for the spatial discretization. The algorithm uses special features of the singularly perturbed convection-diffusion operator. The error due to a local perturbation of the boundary conditions decays extremely fast, in the upwind as well as the crosswind direction, so the overlap in the domain decomposition can be kept to a minimum. The algorithm parallelizes well and is particularly suited for applications in three dimensions. Results of two- and three-dimensional numerical experiments are presented.

Original languageEnglish (US)
Pages (from-to)891-916
Number of pages26
JournalSIAM Journal on Scientific Computing
Issue number3
StatePublished - 2001


  • Convection-diffusion
  • Damping factor
  • Maximum principle
  • Overlapping domain decomposition
  • Upwind finite differences

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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