A Newton-Lanczos Method for Solution of Nonlinear Finite Element Equations.

Abstract

The finite element method reduces nonlinear continuum problems to nonlinear discrete problems which take the form of systems of nonlinear algebraic equations. Attention is devoted to procedures which may be employed to solve the resulting nonlinear algebraic systems. The general class of continuum problems of interest include both material and geometric nonlinearities. Newton's method, modified Newton methods, and quasi-Newton methods are reviewed. However, the technique which has been given focus is the Newton-Lanczos method which is a member of a class of solution methods that employ an iterative, linear equation solver in an inner loop within Newton's method. The Newton-Lanczos algorithm is shown to not only require fewer factorization steps than either the quasi-Newton or modified Newton methods but also possesses more robust convergence characteristics when dealing with nearly singular Jacobian matrices and indefinite systems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1982
Accession Number
ADA112043

Entities

People

  • Bahram Nour-omid

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Civil Engineering
  • Computations
  • Constitutive Equations
  • Continuum Mechanics
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Finite Element Analysis
  • Linear Systems
  • Materials
  • Mechanics
  • Nonlinear Algebraic Equations
  • Numerical Analysis
  • Structural Mechanics
  • Tensile Strength

Fields of Study

  • Mathematics

Readers

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