Local Multiplicative Schwarz Algorithms for Convection-Diffusion Equations.

Abstract

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numericaL examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1995
Accession Number
ADA304195

Entities

People

  • Marcus Sarkis
  • Xiao-chuan Cai

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Algorithms
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Convection
  • Convergence
  • Difference Equations
  • Differential Equations
  • Diffusion
  • Equations
  • Flow
  • Fluid Dynamics
  • Fluid Flow
  • Linear Systems
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)