The University of Southampton
University of Southampton Institutional Repository

Two error bounds for dynamic condensation methods

Two error bounds for dynamic condensation methods
Two error bounds for dynamic condensation methods
The dynamic response of large structural systems is often approximated by condensing the systems into smaller subspaces. Among condensation methods, modal condensation and Krylov projection methods have the capability of generating excellent approximations of the response in a selected frequency band. Here are presented error bounds on the response in the band to complement these and other Galerkin Rayleigh–Ritz condensation methods. The bounds guarantee that the magnitude of the error is below the computed threshold. They are based on the expansion of exact expressions of the error using interior and exterior eigenpairs. The interior error is bounded by using existing error bounds on the interior eigenpairs. Sylvester’s theorem allows one to determine if all interior eigenvalues are approximated. The exterior error is bounded by using the Cauchy–Schwarz inequality and matrices that bound the restriction of the system matrix to the exterior eigenpairs. Two general algorithms are presented as a general framework to compute bounds on the eigenpairs and bounds on the error and the response. They can be specialized to particular implementations of Rayleigh–Ritz and/or Krylov methods. The application of the bounds is illustrated on a variety of condensation methods and problems.
0001-1452
166-176
Lecomte, Christophe
87cdee82-5242-48f9-890d-639a091d0b9c
McDaniel, J. Gregory
77defb64-9502-436e-9287-08533814bcb4
Barbone, Paul E.
20c62a8d-875b-48ce-aa4f-c6a79659fd8f
Lecomte, Christophe
87cdee82-5242-48f9-890d-639a091d0b9c
McDaniel, J. Gregory
77defb64-9502-436e-9287-08533814bcb4
Barbone, Paul E.
20c62a8d-875b-48ce-aa4f-c6a79659fd8f

Lecomte, Christophe, McDaniel, J. Gregory and Barbone, Paul E. (2008) Two error bounds for dynamic condensation methods. AIAA Journal, 46 (1), 166-176. (doi:10.2514/1.29866).

Record type: Article

Abstract

The dynamic response of large structural systems is often approximated by condensing the systems into smaller subspaces. Among condensation methods, modal condensation and Krylov projection methods have the capability of generating excellent approximations of the response in a selected frequency band. Here are presented error bounds on the response in the band to complement these and other Galerkin Rayleigh–Ritz condensation methods. The bounds guarantee that the magnitude of the error is below the computed threshold. They are based on the expansion of exact expressions of the error using interior and exterior eigenpairs. The interior error is bounded by using existing error bounds on the interior eigenpairs. Sylvester’s theorem allows one to determine if all interior eigenvalues are approximated. The exterior error is bounded by using the Cauchy–Schwarz inequality and matrices that bound the restriction of the system matrix to the exterior eigenpairs. Two general algorithms are presented as a general framework to compute bounds on the eigenpairs and bounds on the error and the response. They can be specialized to particular implementations of Rayleigh–Ritz and/or Krylov methods. The application of the bounds is illustrated on a variety of condensation methods and problems.

This record has no associated files available for download.

More information

Published date: January 2008
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 342597
URI: http://eprints.soton.ac.uk/id/eprint/342597
ISSN: 0001-1452
PURE UUID: 71f0a127-219e-4cc2-8466-61710b0dd1eb

Catalogue record

Date deposited: 10 Sep 2012 11:03
Last modified: 14 Mar 2024 11:52

Export record

Altmetrics

Contributors

Author: Christophe Lecomte
Author: J. Gregory McDaniel
Author: Paul E. Barbone

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×