TY - UNPB

T1 - Rational-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots

AU - Bonizzoni, Francesca

AU - Pradovera, Davide

AU - Ruggeri, Michele

PY - 2021/12/8

Y1 - 2021/12/8

N2 - 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 on a different discrete space that resolves the local singularities of the 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 the standard rational interpolation method (SRI), a vector- or function-valued version of it (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 real axis), the spatially adaptive V-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, theV-SRI method seems to be the best-performing one.

AB - 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 on a different discrete space that resolves the local singularities of the 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 the standard rational interpolation method (SRI), a vector- or function-valued version of it (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 real axis), the spatially adaptive V-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, theV-SRI method seems to be the best-performing one.

KW - model order reduction

KW - rational approximation

KW - parametric Helmholtz equation

KW - frequency response

KW - adaptive mesh refinement

U2 - 10.48550/arXiv.2112.04302

DO - 10.48550/arXiv.2112.04302

M3 - Working Paper/Preprint

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

CY - Ithaca, New York

ER -