Ordering Effects on Relaxation Methods Applied to the Discrete Convection-Diffusion Equation

  • Howard C. Elman
  • Michael P. Chernesky
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 60)

Abstract

We present an analysis of relaxation methods for the discrete convection-diffusion equation based on norms of the iteration matrices. For one-dimensional problems, the results show how the performance of iterative solvers is affected by directions of flow associated with the underlying operator. In particular, for problems of size n, relaxation sweeps opposite the direction of flow incur a latency of approximately n steps in which convergence is slow, and red-black relaxation incurs a latency of approximately n/2 steps. There is no latency associated with relaxation that follows the flow. The one-dimensional analysis is also generalized to two-dimensional problems in the case where relaxation follows the flow.

Keywords

Convection Univer 

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Copyright information

© Springer-Verlag New York, Inc 1994

Authors and Affiliations

  • Howard C. Elman
    • 1
    • 2
  • Michael P. Chernesky
    • 3
  1. 1.Department of Computer ScienceUniversity of MarylandCollege ParkUSA
  2. 2.Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA
  3. 3.Department of MathematicsUniversity of MarylandCollege ParkUSA

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