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Pade approximants and the modal connection: Towards increased robustness for fast parametric sweeps
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
2018 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 113, no 1, p. 65-81Article in journal (Refereed) Published
Abstract [en]

To increase the robustness of a Pade-based approximation of parametric solutions to finite element problems, an a priori estimate of the poles is proposed. The resulting original approach is shown to allow for a straightforward, efficient, subsequent Pade-based expansion of the solution vector components, overcoming some of the current convergence and robustness limitations. In particular, this enables for the intervals of approximation to be chosen a priori in direct connection with a given choice of Pade approximants. The choice of these approximants, as shown in the present work, is theoretically supported by the Montessus de Ballore theorem, concerning the convergence of a series of approximants with fixed denominator degrees. Key features and originality of the proposed approach are (1) a component-wise expansion which allows to specifically target subsets of the solution field and (2) the a priori, simultaneous choice of the Pade approximants and their associated interval of convergence for an effective and more robust approximation. An academic acoustic case study, a structural-acoustic application, and a larger acoustic problem are presented to demonstrate the potential of the approach proposed.

Place, publisher, year, edition, pages
John Wiley & Sons, 2018. Vol. 113, no 1, p. 65-81
Keywords [en]
fast frequency sweeps, finite element method, Pade approximants, reduced-order model, structural-acoustics
National Category
Mathematics Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-220448DOI: 10.1002/nme.5603ISI: 000417595300004Scopus ID: 2-s2.0-85028912343OAI: oai:DiVA.org:kth-220448DiVA, id: diva2:1170502
Funder
EU, FP7, Seventh Framework Programme, 2015-04925VINNOVA, 2016-05195
Note

QC 20180103

Available from: 2018-01-03 Created: 2018-01-03 Last updated: 2018-05-07Bibliographically approved

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