Numerical methods for time-harmonic wave phenomena are often computationally intensive, leading to high simulation costs, e.g., in outer-loop applications like design optimization and uncertainty quantification. In this framework, model order reduction methods can be used to obtain cheap and reliable approximations of the expensive high-fidelity problem.
On one hand, intrusive algorithms like implicit moment matching and reduced bases can be applied to obtain a surrogate model by (quasi-)optimal projection of the original problem onto a low-dimensional subspace. On the other hand, non-intrusive methods like vector fitting and Loewner framework build a rational approximation of the solution (wrt frequency) without the need to access the high-fidelity problem. However, this usually comes at the cost of "oversampling", i.e., solving the expensive high-fidelity problem more times than is necessary with, e.g., intrusive methods.
In this talk, we describe the recently proposed "minimal rational interpolation" method, which combines some advantages of intrusive and non-intrusive methods. Particularly, we showcase a strategy for adaptive frequency sampling, which mimics the weak-greedy reduced basis method without the need for intrusiveness.