Truncated newton methods for nonlinear finite element analysis

Papadrakakis, M; Gantes, CJ

dc.contributor.author	Papadrakakis, M	en
dc.contributor.author	Gantes, CJ	en
dc.date.accessioned	2014-03-01T01:07:19Z
dc.date.available	2014-03-01T01:07:19Z
dc.date.issued	1988	en
dc.identifier.issn	0045-7949	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9930
dc.subject	Approximate Solution	en
dc.subject	Convergence Rate	en
dc.subject	Degree of Freedom	en
dc.subject	Direct Method	en
dc.subject	Exact Solution	en
dc.subject	Finite Element	en
dc.subject	Finite Element Mesh	en
dc.subject	Finite Element Method	en
dc.subject	Iteration Method	en
dc.subject	Iterative Solution	en
dc.subject	Large Scale	en
dc.subject	Large-scale Problem	en
dc.subject	Line Search	en
dc.subject	Linear Equations	en
dc.subject	Linear System of Equations	en
dc.subject	Local Convergence	en
dc.subject	Newton Iteration	en
dc.subject	Nonlinear Finite Element Analysis	en
dc.subject	Nonlinear Problem	en
dc.subject	Potential Energy	en
dc.subject	Preconditioned Conjugate Gradient	en
dc.subject	Structure Analysis	en
dc.subject	Taylor Series Expansion	en
dc.subject	Truncated Newton Method	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Engineering, Civil	en
dc.title	Truncated newton methods for nonlinear finite element analysis	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/0045-7949(88)90306-9	en
heal.identifier.secondary	http://dx.doi.org/10.1016/0045-7949(88)90306-9	en
heal.language	English	en
heal.publicationDate	1988	en
heal.abstract	In the present study procedures for the solution of large-scale nonlinear algebraic discrete equations arising from the application of the finite element method to structural analysis problems are described and evaluated. The methods are based on Newton's method for the outer iterations, while for the linearized problem in each iteration the preconditioned conjugate gradient (CG) method is employed. This combination for the outer and inner iterations allows the use of less accuracy in computing exact Newton directions when far from the solution and the gradual increase in accuracy for the inner loops as the final solution is approached. This technique leads to the truncated Newton methods. Two preconditioning techniques for CG have been described and compared, namely the partial preconditioning and the partial elimination. Both techniques use a drop-off parameter ψ to control the computer storage demands for the extra matrix required. The results of two test examples are very encouraging as they show that the proposed method can be very effective in the solution of nonlinear finite element problems. © 1988.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Computers and Structures	en
dc.identifier.doi	10.1016/0045-7949(88)90306-9	en
dc.identifier.isi	ISI:A1988R118800033	en
dc.identifier.volume	30	en
dc.identifier.issue	3	en
dc.identifier.spage	705	en
dc.identifier.epage	714	en