Termination criteria for inexact fixedpoint schemes
(2015) In Numerical Linear Algebra with Applications 22(4). p.702716 Abstract
 We analyze inexact fixedpoint iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixedpoint iteration. Important applications are the Picard iteration and partitioned fluidstructure interaction. For the analysis, the iteration is modeled as a perturbed fixedpoint iteration, and existing analysis is extended to the nested case x=F(S(x)). We prove that if the iteration converges, it converges to the exact solution irrespective of the tolerance in the inner systems, provided that a nonstandard relative termination criterion is employed, whereas standard relative and absolute criteria do not have... (More)
 We analyze inexact fixedpoint iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixedpoint iteration. Important applications are the Picard iteration and partitioned fluidstructure interaction. For the analysis, the iteration is modeled as a perturbed fixedpoint iteration, and existing analysis is extended to the nested case x=F(S(x)). We prove that if the iteration converges, it converges to the exact solution irrespective of the tolerance in the inner systems, provided that a nonstandard relative termination criterion is employed, whereas standard relative and absolute criteria do not have this property.
Numerical results demonstrate the effectiveness of the approach with the nonstandard termination criterion. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/5277077
 author
 Birken, Philipp ^{LU}
 organization
 publishing date
 2015
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 fixedpoint iteration, Picard iteration, transmission problem, Dirichletâ€“Neumann iteration, termination criteria
 in
 Numerical Linear Algebra with Applications
 volume
 22
 issue
 4
 pages
 702  716
 publisher
 WileyBlackwell
 external identifiers

 wos:000357833700007
 scopus:84935757636
 ISSN
 10705325
 DOI
 10.1002/nla.1982
 language
 English
 LU publication?
 yes
 id
 f26bdfeb5fa84c67aaf220ed9198902c (old id 5277077)
 date added to LUP
 20150427 10:11:59
 date last changed
 20171022 03:21:21
@article{f26bdfeb5fa84c67aaf220ed9198902c, abstract = {We analyze inexact fixedpoint iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixedpoint iteration. Important applications are the Picard iteration and partitioned fluidstructure interaction. For the analysis, the iteration is modeled as a perturbed fixedpoint iteration, and existing analysis is extended to the nested case x=F(S(x)). We prove that if the iteration converges, it converges to the exact solution irrespective of the tolerance in the inner systems, provided that a nonstandard relative termination criterion is employed, whereas standard relative and absolute criteria do not have this property.<br/><br> Numerical results demonstrate the effectiveness of the approach with the nonstandard termination criterion.}, author = {Birken, Philipp}, issn = {10705325}, keyword = {fixedpoint iteration,Picard iteration,transmission problem,Dirichletâ€“Neumann iteration,termination criteria}, language = {eng}, number = {4}, pages = {702716}, publisher = {WileyBlackwell}, series = {Numerical Linear Algebra with Applications}, title = {Termination criteria for inexact fixedpoint schemes}, url = {http://dx.doi.org/10.1002/nla.1982}, volume = {22}, year = {2015}, }