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.
%0 Journal Article
%1 GosGU21
%A Gosea, Ion Victor
%A Gugercin, Serkan
%A Unger, Benjamin
%D 2021
%J ArXiv e-print 2104.01016
%K exc2075 from:benjaminunger myown pn4 preprint
%T Parametric model reduction via rational interpolation along parameters
%U https://arxiv.org/abs/2104.01016
%X 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.
@article{GosGU21,
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.},
added-at = {2021-12-08T17:10:08.000+0100},
author = {{Gosea}, Ion Victor and {Gugercin}, Serkan and {Unger}, Benjamin},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2d3572f26476603601acfdc546ca1d55c/katharinafuchs},
interhash = {4df371c821dccf6862044ef45cd25139},
intrahash = {d3572f26476603601acfdc546ca1d55c},
journal = {ArXiv e-print 2104.01016},
keywords = {exc2075 from:benjaminunger myown pn4 preprint},
pubdate = {2021-04-05},
timestamp = {2021-12-08T16:10:08.000+0100},
title = {Parametric model reduction via rational interpolation along parameters},
url = {https://arxiv.org/abs/2104.01016},
year = 2021
}
