Dipartimento di Matematica ''F. Casorati''

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Padé-based Model Order Reduction for Helmholtz frequency responses

Dr. Francesca Bonizzoni, Università di Vienna

Sala conferenze IMATI-CNR, Pavia - Martedì 9 Gennaio 2018 h.16:30

Abstract. Due to the oscillatory behavior of the analytic solutions, the finite element approximation of the Helmholtz boundary value problem in mid- and high-frequency regimes is computational expensive and time-consuming: accurate approximations are possible only on very fine meshes or with high polynomial approximation degrees. For this reason, when solutions at many frequencies are of interest, repeated finite element computations become prohibitive.

To reduce the computational cost we propose a model order reduction method based on Least Square Padé-type techniques. In particular, the Helmholtz frequency response map - which associates each frequency with the corresponding solution of the Helmholtz boundary value problem - is approximated starting only from precomputed evaluations at few frequency values.
Uniform convergence results of the Least Square Padé approximation error are proved. Two algorithms to compute the Least Square Padé approximant are discussed. 2D numerical tests are provided that confirm the theoretical upper bound on the convergence error.

This is joint work with Fabio Nobile (EPFL) and Ilaria Perugia (University of Vienna).

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Dipartimento di Matematica ''F. Casorati''

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