Parametric model reduction via rational interpolation along parameters

TL;DR

This paper introduces a new parametric model reduction method that interpolates transfer functions along parameter-dependent curves using holomorphic projection spaces, enabling more flexible and continuous parameter interpolation.

Contribution

It develops a novel projection-based framework for parametric system reduction that interpolates transfer functions along curves rather than discrete points, with holomorphic properties proven for system matrices.

Findings

Effective interpolation along parameter curves demonstrated

Holomorphic properties of projection spaces established

Numerical examples validate the approach

Abstract

We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the standard approach where transfer function interpolation is achieved for a discrete set of parameter and frequency samples. We accomplish this goal by using parameter-dependent projection spaces. Our main result shows that for holomorphic system matrices, the corresponding interpolatory projection spaces are also holomorphic. The coefficients of the power series representation of the projection spaces can be computed iteratively using standard methods. We illustrate the analysis on three numerical examples.