Titel
Least-Squares Padé approximation of parametric and stochastic Helmholtz maps
Fabio Nobile
CSQI – MATH, Ecole Polytechnique Fédérale de Lausanne
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Abstract
The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 2020). Algorithmical aspects concerning the construction of rational LS-Padé approximants are described. In particular, we show that the computation of the Padé denominator can be carried out efficiently by solving an eigenvalue-eigenvector problem involving a Gramian matrix. The LS-Padé techniques are employed to approximate the frequency response map associated with two parametric time-harmonic acoustic wave problems, namely a transmission-reflection problem and a scattering problem. In both cases, we establish the meromorphy of the frequency response map. The Helmholtz equation with stochastic wavenumber is also considered. In particular, for Lipschitz functionals of the solution and their corresponding probability measures, we establish weak convergence of the measure derived from the LS-Padé approximant to the true one. 2D numerical tests are performed, which confirm the effectiveness of the approximation methods.
Stichwort
Hilbert space-valued meromorphic mapsPadé approximantsConvergence of Padé approximantsParametric Helmholtz equationPDE with random coefficients
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Advances in Computational Mathematics
Band
46
Ausgabe
3
ISSN
1019-7168
Erscheinungsdatum
2020
Publication
Springer Science and Business Media LLC
Erscheinungsdatum
2020
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2020
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