A Simplified Analysis of the Multigrid V-Cycle as a Fast Elliptic Solver

Abstract

For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining multigrid convergence rate estimates for cycles involving more than two grids -- using essentially the same analysis as for the two-grid cycle. For the simple case of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by te variational theory. Both theoretical justification and experimental evidence are presented.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1988
Accession Number
ADA202973

Entities

People

  • Naomi H. Decker
  • Shlomo Ta'asan

Tags

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Computer Science
  • Computers
  • Convergence
  • Engineering
  • Equations
  • Error Analysis
  • Errors
  • Fourier Analysis
  • Interpolation
  • Iterations
  • Mathematics
  • Notation
  • Two Dimensional
  • United States
  • Virginia

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science (Mechanical Engineering).