Arc-Length Continuation and Multi-Grid Techniques for Nonlinear Elliptic Eigenvalue Problems,

Abstract

We investigate multi-grid methods for solving linear systems arising from arc-length continuation techniques applied to nonlinear elliptic eigenvalue problems. We find that the usual multi-grid methods diverge in the neighborhood of singular points of the solution branches. As a result, the continuation method is unable to continue past a limit point in the Bratu problem. This divergence is analysed and a modified multi-grid algorithm has been devised based on this analysis. In principle, this new multi-grid algorithm converges for elliptic systems arbitrarily close to singularity and has been successfully in conjunction with arc-length continuation procedures on the model problem. In the worst situation, both the storage and the computational work are only about a factor of two more than the unmodified multi-grid methods. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 19, 1981
Accession Number
ADA098718

Entities

People

  • H. B. Keller
  • Tony F. C. Chan

Organizations

  • Florida State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Fluid Mechanics
  • Frequency
  • Linear Algebra
  • Linear Systems
  • Numerical Analysis
  • Partial Differential Equations
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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