A phase error analysis of multigrid methods for hyperbolic equations

W. L. Wan*, Tony F. Chan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this paper, we study the effects of the coarse grid correction process on multi grid convergence for hyperbolic problems in one and two dimensions. We approach this from the perspective of phase error, which allows us to exploit the hyperbolic nature of the underlying PDE. In particular, we consider three combinations of coarse grid operators and coarse grid solution ap proaches: (1) inexact coarse grid solve with direct discretization, (2) exact coarse grid solve with direct discretization, and (3) exact coarse grid solve with Galerkin coarse grid operator. For all these approaches, we show that the convergence behavior of multigrid can be precisely described by the phase error analysis of the coarse grid correction matrix, and we verify our results by numerical examples in one and two dimensions.

Original languageEnglish (US)
Pages (from-to)857-880
Number of pages24
JournalSIAM Journal on Scientific Computing
Volume25
Issue number3
DOIs
StatePublished - Nov 1 2003
Externally publishedYes

Keywords

  • Fourier analysis
  • Hyperbolic equations
  • Multigrid
  • Phase error

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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