Chasing resonances with adaptive rational approximation
Vortrag von Dr. Davide Pradovera
Datum: 15.10.25 Zeit: 16.30 - 18.00 Raum: ETH HG G 19.2
Frequency-domain models of wave propagation and vibration phenomena often give rise to large-scale linear systems and (potentially nonlinear) eigenvalue problems, whose solution is essential for tasks such as resonance analysis, design optimization, or uncertainty quantification. High-fidelity simulations, however, are typically too costly to be used directly in such applications. Model reduction and surrogate modeling thus play a central role. In this talk, we focus on rational approximation techniques that able to adaptively target the spectral features of interest. Building on ideas from reduced basis methods, we describe the "minimal rational interpolation" strategy, which adaptively selects frequency samples to construct accurate surrogates without oversampling. This allows us to approximate resonances efficiently and reliably. We further discuss how the same perspective can be leveraged to address parametric eigenvalue problems, where additional parameters are introduced to model, e.g., material or geometry variations or uncertainties. In such problems, eigenvalue manifolds may exhibit crossings, bifurcations, or even discontinuities as parameters vary. Our approach combines adaptive rational approximation with contour-integration-based eigensolvers to synthesize these manifolds in a robust way. This talk will cover joint work with Alessandro Borghi (TU Berlin), Ralf Hiptmair (ETH Zurich), and Ilaria Perugia (U Vienna).