Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots

Bonizzoni, Francesca and Pradovera, Davide and Ruggeri, Michele (2023) Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots. Mathematics in Engineering, 5 (4). pp. 1-38. ISSN 2640-3501 (https://doi.org/10.3934/mine.2023074)

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Abstract

We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite elements, so that each snapshot lives in a different discrete space that resolves the local singularities of the analytical solution and is adjusted to the considered frequency value. A rational surrogate is then assembled adopting either a least squares or an interpolatory approach, yielding a function-valued version of the standard rational interpolation method (V-SRI) and the minimal rational interpolation method (MRI). In the context of building an approximation for linear or quadratic functionals of the Helmholtz solution, we perform several numerical experiments to compare the proposed methodologies. Our simulations show that, for interior resonant problems (whose singularities are encoded by poles on the V-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, the V-SRI method seems to be the best performing one.

ORCID iDs

Bonizzoni, Francesca, Pradovera, Davide and Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602;
CORE (COnnecting REpositories)