Convergence Analysis and Acceleration of the Schwartz Alternating Method,

Abstract

The convergence rate of the Schwarz Alternating Method(SAM) is studied for applications involving the solution of elliptic equations on composite grids. Such problems arise when solvers which can only be used on special domains, such as rectangles, are used for more general region; and in the disection of problems for parallel processing. It is shown that the convergence rate is a function of the overlap, number and shape of the subregions into which the problem domain is divided. The convergence rates for SAM are slow and an accelerated method based on overrelaxation techniques is developed. The SAM analysis is extended to predict the performance of the accelerated method and optimal relaxation parameters. Finally, we study the effects of changing the iteration order for the SAM and accelerated SAM methods.

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Document Details

Document Type
Technical Report
Publication Date
Aug 26, 1986
Accession Number
ADA173961

Entities

People

  • Joseph Oliger
  • Wei-pai Tang
  • William Skamarock

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Composite Materials
  • Computations
  • Convergence
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Equations
  • Errors
  • Geometry
  • Iterations
  • Parallel Computing
  • Parallel Processing
  • Partial Differential Equations
  • Poisson Equation
  • Two Dimensional

Readers

  • Approximation Theory.
  • Linear Algebra
  • Structural Health Monitoring of Composite Structures.