Fourier-Laplace Analysis of Multigrid Waveform Relaxation Method for Hyperbolic Equations.

Abstract

The multigrid waveform relaxation (WR) algorithm has been fairly studied and implemented for parabolic equations. It has been found that the performance of the multigrid WR method for a parabolic equation is practically the same as that of multigrid iteration for the associated steady state elliptic equation. However, the properties of the multigrid WR method for hyperbolic problems are relatively unknown. This paper studies the multigrid acceleration to the WR iteration for hyperbolic problems, with a focus on the convergence comparison between the multigrid WR iteration and the multigrid iteration for the corresponding steady state equations. Using a Fourier-Laplace analysis in two case studies, it is found that the multigrid performance on hyperbolic problems no longer shares the close resemblance in convergence factors between the WR iteration for parabolic equations and the iteration for the associated steady state equations.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1996
Accession Number
ADA317391

Entities

People

  • Hong Zhang
  • Shlomo Ta'asan

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Case Studies
  • Computational Fluid Dynamics
  • Computational Science
  • Convergence
  • Differential Equations
  • Engineering
  • Equations
  • Equations Of State
  • Fluid Dynamics
  • Fourier Analysis
  • Frequency
  • Iterations
  • Mathematics
  • Partial Differential Equations
  • Steady State
  • Waveforms

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)