A Survey of Preconditioners for Domain Decomposition.

Abstract

This document studies domain decomposition techniques for the solution of partial differential equations on a domain divided into several subdomains. These techniques have special applications in the solution of elliptic problems on irregular domains and parallel computation. A unifying feature of these techniques is the use of preconditioned conjugate gradient method in solving for the unknowns on the interfaces of the subdomains, or in some cases, on the whole domain. Since each iteration involves solving problems on each subdomain, it is essential to keep the number of iterations low. For this reason, much effort has been devoted recently to the construction of good preconditioners for the conjugate gradient methods. This paper surveys the most common preconditioners that have appeared in the literature, including a new class that we have developed recently. One objective is to illuminate the relationships among these preconditioners. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1985
Accession Number
ADA168757

Entities

People

  • Diana C. Resasco
  • Tony F. Chan

Organizations

  • Yale University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Aspect Ratio
  • Boundaries
  • Capacitance
  • Coefficients
  • Computations
  • Computer Science
  • Decomposition
  • Differential Equations
  • Eigenvalues
  • Equations
  • Helmholtz Equations
  • Iterations
  • Numerical Analysis
  • Parallel Computing
  • Parallel Processing
  • Partial Differential Equations
  • Poisson Equation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research
  • Theoretical Analysis.