Padé approximants and the modal connection: Towards increased robustness for fast parametric sweeps |
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| Authors: | Romain Rumpler |
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| Affiliation: | Marcus Wallenberg Laboratory for Sound and Vibration Research, Department of Aeronautical and Vehicle Engineering, School of Engineering Sciences, KTH Royal Institute of Technology, SE‐100 44 Stockholm, Sweden |
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| Abstract: | To increase the robustness of a Padé‐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 Padé‐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 Padé 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 Padé 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. |
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| Keywords: | fast frequency sweeps finite element method Padé approximants reduced‐order model structural‐acoustics |
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