Massively Parallel Iterative Methods: Multiscale Preconditioners and Implicit Methods.

Abstract

Nonlinear and linear systems of equations often arise in scientific computation, for example in implicit methods in Computational Fluid Dynamics (CFD). It is important to find cost-effective and accurate methods to solve such systems. Iterative methods are among those widely used, especially for 3D problems. In this project, we consider iterative methods which are especially suited to massively parallel architectures. To accelerate convergence of these iterative methods, preconditioners are often used. Good preconditioners reduce the number of iterations and involves few arithmetic operations per iteration. Effective parallel preconditioners must account for the global coupling inherent in elliptic problems. On the other hand, efficient parallel implementation often favors local computations. Multiscale iterative methods represent a good compromise between these two conflicting goals. We focused our attention on two classes of multiscale preconditioners: multilevel basis preconditioners and domain decomposition preconditioners.

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Document Details

Document Type
Technical Report
Publication Date
Mar 22, 1995
Accession Number
ADA295790

Entities

People

  • Tony F. Chan

Organizations

  • University of California, Los Angeles

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Composite Materials
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Convergence
  • Decomposition
  • Equations
  • Fluid Dynamics
  • Galerkin Method
  • Geometry
  • Image Processing
  • Linear Algebra
  • Linear Systems
  • Parallel Computing

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)
  • Systems Analysis and Design