Analysis of Domain Decomposition Preconditioners on L-Shaped and C- Shaped Regions

Abstract

This document presents an algebraic analysis of some domain decomposition preconditioners on irregular regions. The authors analyze a preconditioner proposed in another work for the interface system and prove that, for all L-shaped regions and some C-shaped regions, it produces a convergence rate that is independent of the size of the discretization and the relative shape of the subdomains (aspect ratios). Specifically, it is proven that the condition number of the preconditioned capacitance system is bound by 2.16 for all L-shaped domains. Some results for other simple irregular geometries are also given.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1988
Accession Number
ADA199806

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
  • Computer Science
  • Convergence
  • Decomposition
  • Differential Equations
  • Eigenvalues
  • Equations
  • Fourier Analysis
  • Iterations
  • Linear Systems
  • Numbers
  • Partial Differential Equations
  • Poisson Equation
  • Theorems

Readers

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