Multigrid Applied to Singular Perturbation Problems.

Abstract

The solution of the singular perturbation problem (epsilon u <2 primers> + b(x) u <one primer> = f, 0<x<1 with 1>>e>0, u(0)=u sub0, u(1)=u1 by a multigrid algorithm is considered. Theoretical and experimental results for a number of different discretizations are presented. The theoretical and observed rates agree with the results developed in an earlier work. In addition, the rate of convergence of the algorithm when the coarse grid operator is the natural finite difference analogue of the fine grid operator is presented. This is in contrast to the case on the previous work where the Galerkin choice (I subscript H sub h) (L sub h) (I subscript h sub H).

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1987
Accession Number
ADA189081

Entities

People

  • David Kamowitz

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Computations
  • Convergence
  • Eigenvalues
  • Engineering
  • Equations
  • Errors
  • Iterations
  • Linear Systems
  • Notation
  • Numerical Analysis
  • Perturbations

Fields of Study

  • Mathematics
  • Physics

Readers

  • Analytical Mechanics
  • Computational Fluid Dynamics (CFD)
  • Mathematical Modeling and Probability Theory.