
Accession Number : ADA112043
Title : A NewtonLanczos Method for Solution of Nonlinear Finite Element Equations.
Descriptive Note : Rept. for MarOct 81,
Corporate Author : CALIFORNIA UNIV BERKELEY DEPT OF CIVIL ENGINEERING
Personal Author(s) : NourOmid,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 quasiNewton methods are reviewed. However, the technique which has been given focus is the NewtonLanczos 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 NewtonLanczos algorithm is shown to not only require fewer factorization steps than either the quasiNewton 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