Accession Number : ADA112043

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

Descriptive Note : Rept. for Mar-Oct 81,


Personal Author(s) : Nour-Omid,Bahram

PDF Url : ADA112043

Report Date : Feb 1982

Pagination or Media Count : 65

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)

Descriptors :   *Finite element analysis, Nonlinear algebraic equations, Algorithms, Continuum mechanics, Structural mechanics

Subject Categories : Theoretical Mathematics
      Structural Engineering and Building Technology

Distribution Statement : APPROVED FOR PUBLIC RELEASE