Bifurcation detection with the (un)preconditioned GMRES(m)

Spyropoulos, AN; Palyvos, JA; Boudouvis, AG

dc.contributor.author	Spyropoulos, AN	en
dc.contributor.author	Palyvos, JA	en
dc.contributor.author	Boudouvis, AG	en
dc.date.accessioned	2014-03-01T01:19:56Z
dc.date.available	2014-03-01T01:19:56Z
dc.date.issued	2004	en
dc.identifier.issn	0045-7825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15782
dc.subject	Arnoldi's method	en
dc.subject	Bifurcation detection	en
dc.subject	Deflation	en
dc.subject	GMRES	en
dc.subject	Newton's method	en
dc.subject	Preconditioner	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Condition monitoring	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Iterative methods	en
dc.subject.other	Laplace transforms	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Problem solving	en
dc.subject.other	Bifurcation point detection	en
dc.subject.other	Iterative solvers	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	bifurcation	en
dc.title	Bifurcation detection with the (un)preconditioned GMRES(m)	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cma.2004.04.002	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cma.2004.04.002	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	When iterative solvers are used for the solution of the linearized equations sets arising from Newton's method, detection of bifurcation points in the solution space can be done by solving several eigenvalue problems with the Jacobian matrix during parameter continuation. Monitoring the condition number of appropriate matrices involved in the GMRES method employed here, replaces or significantly reduces the costly eigenvalue computations. The effectiveness of the detection method is examined in connection with the usage of unpre- and preconditioned iterative solvers. (C) 2004 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE SA	en
heal.journalName	Computer Methods in Applied Mechanics and Engineering	en
dc.identifier.doi	10.1016/j.cma.2004.04.002	en
dc.identifier.isi	ISI:000224241400011	en
dc.identifier.volume	193	en
dc.identifier.issue	42-44	en
dc.identifier.spage	4707	en
dc.identifier.epage	4716	en