Parametric model order reduction for large-scale systems using Krylov subspace

In this work, we propose a method for reduced order models that preserve the physical parameters and therefore enable the optimization of the design parameters, material properties or geometries. More specifically, for an arbitrary rational transfer function $G(s,p)\(in the complex variables s and parameter p, we aim to find a low order rational \)G_r(s,p)\(that matches the moments in both frequencies and design parameters at dedicated points\)\mathcal{S}:=\{s_1,\dots,s_k\} \subset \mathbb{C}\(and \)\mathcal{P}:=\{p_1,\dots,p_{\ell}\}\subset \mathbb{R}$. We construct the projection matrices along these two sets. An a-priori error bound has been derived that represents the local accuracy of the reduced model's transfer function nearby the points $\mathcal{S}\times \mathcal{P}$. Furthermore, this error bound allows for finding the optimal expansion points and truncation order. Simulation results show that both time domain and frequency domain indicate that the proposed method delivers good matching and outperforms the previous work.