Numerical methods for time-harmonic wave propagation phenomena are often computationally intensive. In this framework, model reduction methods can be used to obtain a cheap and reliable approximation of the frequency response of the system. In this talk, we consider parametric frequency response problems, where the high-fidelity problem depends not only on the frequency, but also on additional design/uncertain parameters. We describe an original model reduction approach that can be applied non-intrusively in this setting.
Our method first builds a database of frequency-response surrogate models via minimal rational interpolation, by freezing the extra parameters. Then, the different frequency-dependent surrogate models are combined over parameter space. This requires special care due to the rational nature of the surrogates. The exploration of the (potentially, high-dimensional) parameter space is carried out via locally adaptive sparse grids, through which one can weaken the curse of dimention while sampling parameter configurations in an adaptive way.
This is joint work with Fabio Nobile.