Change search
ReferencesLink to record
Permanent link

Direct link
An adaptive strategy for the bivariate solution of finite element problems using multivariate nested Pade approximants
Creo Dynam AB, Sweden.ORCID iD: 0000-0002-6555-531X
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.ORCID iD: 0000-0003-1855-5437
Trinity College, Department of Mechanical and Manufacturing Engineering, Ireland.
2014 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 100, no 9, 689-710 p.Article in journal (Refereed) Published
Abstract [en]

Most engineering applications involving solutions by numerical methods are dependent on several parameters, whose impact on the solution may significantly vary from one to the other. At times an evaluation of these multivariate solutions may be required at the expense of a prohibitively high computational cost. In the present paper, an adaptive approach is proposed as a way to estimate the solution of such multivariate finite element problems. It is based upon the integration of so-called nested Pade approximants within the finite element procedure. This procedure includes an effective control of the approximation error, which enables adaptive refinements of the converged intervals upon reconstruction of the solution. The main advantages lie in a potential reduction of the computational effort and the fact that the level of a priori knowledge required about the solution in order to have an accurate, efficient, and well-sampled estimate of the solution is low. The approach is introduced for bivariate problems, for which it is validated on elasto-poro-acoustic problems of both academic and more industrial scale. It is argued that the methodology in general holds for more than two variables, and a discussion is opened about the truncation refinements required in order to generalize the results accordingly.

Place, publisher, year, edition, pages
2014. Vol. 100, no 9, 689-710 p.
Keyword [en]
multivariate Pade approximants, reduced-order model, solution expansion, finite element method
National Category
Mathematics Other Engineering and Technologies
URN: urn:nbn:se:kth:diva-157027DOI: 10.1002/nme.4777ISI: 000344005000003ScopusID: 2-s2.0-84920069236OAI: diva2:768833

QC 20141205

QC 20160921

Available from: 2014-12-05 Created: 2014-12-04 Last updated: 2016-09-21Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Rumpler, RomainGöransson, Peter
By organisation
Marcus Wallenberg Laboratory MWL
In the same journal
International Journal for Numerical Methods in Engineering
MathematicsOther Engineering and Technologies

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 42 hits
ReferencesLink to record
Permanent link

Direct link