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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, Skolan för teknikvetenskap (SCI), Farkost och flyg, MWL Marcus Wallenberg Laboratoriet.ORCID-id: 0000-0003-1855-5437
Trinity College, Department of Mechanical and Manufacturing Engineering, Ireland.
2014 (engelsk)Inngår i: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 100, nr 9, s. 689-710Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2014. Vol. 100, nr 9, s. 689-710
Emneord [en]
multivariate Pade approximants, reduced-order model, solution expansion, finite element method
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-157027DOI: 10.1002/nme.4777ISI: 000344005000003Scopus ID: 2-s2.0-84920069236OAI: oai:DiVA.org:kth-157027DiVA, id: diva2:768833
Merknad

QC 20141205

QC 20160921

Tilgjengelig fra: 2014-12-05 Laget: 2014-12-04 Sist oppdatert: 2017-12-05bibliografisk kontrollert

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Rumpler, RomainGöransson, Peter

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