Accelerated Convergence of Structures Banded Systems Using Constrained Corrections

Abstract

Descretization of fluid flow equations results in a structured banded system of equations. Interative methods used to solve such a system transfer information rapidly between neighboring points but exhibit slow global communication when the system is large. This phenomenon results in a slow convergence with the asymptotic stages showing a spatially smooth behavior for the errors, iterative corrections, and residuals. This smooth behavior is exploited by approximating the error and corrections with an interpolation over a selected subset of the grid. A variational form is used to compress the original system of equations into a smaller system. This compression is repeated through several levels of grid sizes to obtain a dramatic improvement in convergence rate. A relaxation parameter is dynamically calculated at each step with a negligible increase in computational effort. Although the method was developed for solving full potential flow using a variational principle, it is applicable to other problems with the structured banded property.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1981
Accession Number
ADA108805

Entities

People

  • Karl Kneile

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Aspect Ratio
  • Boundaries
  • Compression
  • Convergence
  • Engineering
  • Equations
  • Flow
  • Geometry
  • Interpolation
  • Linear Systems
  • Potential Flow
  • Security
  • Three Dimensional
  • Two Dimensional
  • United States
  • Variational Principles

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Approximation Theory.
  • Computational Fluid Dynamics (CFD)