Accelerating an inexact Newton/GMRES scheme by subspace decomposition

Pashos, G; Koronaki, ED; Spyropoulos, AN; Boudouvis, AG

dc.contributor.author	Pashos, G	en
dc.contributor.author	Koronaki, ED	en
dc.contributor.author	Spyropoulos, AN	en
dc.contributor.author	Boudouvis, AG	en
dc.date.accessioned	2014-03-01T01:32:36Z
dc.date.available	2014-03-01T01:32:36Z
dc.date.issued	2010	en
dc.identifier.issn	0168-9274	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20186
dc.subject	Bratu	en
dc.subject	Eigenproblem	en
dc.subject	GMRES	en
dc.subject	Lid-driven cavity	en
dc.subject	Navier-Stokes	en
dc.subject	RPM	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Eigenproblem	en
dc.subject.other	Eigenspaces	en
dc.subject.other	Element method	en
dc.subject.other	Iterative solvers	en
dc.subject.other	Lid-driven cavities	en
dc.subject.other	Navier Stokes	en
dc.subject.other	Newton iterations	en
dc.subject.other	Newton's methods	en
dc.subject.other	Nonlinear algebraic equations	en
dc.subject.other	Physical model	en
dc.subject.other	Preconditioners	en
dc.subject.other	Projection method	en
dc.subject.other	Subspace decomposition	en
dc.subject.other	Algebra	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Linear systems	en
dc.subject.other	Magnetic storage	en
dc.subject.other	Navier Stokes equations	en
dc.subject.other	Newton-Raphson method	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Nonlinear equations	en
dc.title	Accelerating an inexact Newton/GMRES scheme by subspace decomposition	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.apnum.2009.08.003	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.apnum.2009.08.003	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	A technique for accelerating inexact Newton schemes is presented for the solution of nonlinear systems of algebraic equations that is based on the so-called recursive projection method (RPM) and is built as a computational shell around a Newton/Krylov code. The method acts directly on the 'outer' Newton iteration and does not act as a preconditioner to accelerate the solution of the linear system, i.e. the 'inner' Krylov iteration. The advantage of this approach is that it reduces the number of Newton iterations that are needed for convergence while still performing inexpensive Krylov iterations for the solution of the linear system at each Newton step. The method can be applied in conjunction with a preconditioned or unpreconditioned Krylov iterative solver, serial or parallel, of any discretized physical model. In addition, it enables the extraction of the dominant eigenspace with the help of a low-dimensional Jacobian matrix that is formulated in the course of the iterations making the solution of a large-scale eigenproblem, unnecessary. The proposed approach is applied on the 2-d Bratu problem and the lid-driven cavity problem. The equations are discretized with the Galerkin/finite element method and the resulting nonlinear algebraic equation set is solved by Newton's method. At each Newton step the restarted generalized minimum residual or GMRES(m) procedure is implemented for the solution of the resulting linear equation set. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Applied Numerical Mathematics	en
dc.identifier.doi	10.1016/j.apnum.2009.08.003	en
dc.identifier.isi	ISI:000277031000008	en
dc.identifier.volume	60	en
dc.identifier.issue	4	en
dc.identifier.spage	397	en
dc.identifier.epage	410	en