IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

## Ninth Annual Graduate Student Mini-conference in Computational Mathematics

Alexander Grimm
Virginia Tech
Reduced order models play a significant role in simulation, design and optimization as they are able to reduce the computational complexity drastically while retaining accuracy. Interpolatory model reduction is one of the widely used methods where transfer function of the reduced model interpolates that of the original at carefully selected frequency domain interpolation points. Indeed, for linear nonparametric dynamical system, Iterative Rational Krylov Algorithm chooses these points optimally in the $\mathcal{H} _ 2$ norm. Even though interpolatory methods have been extended to parametric systems, except for special cases, there exists no optimal selection strategy for frequency and parameter interpolation points jointly for a combined error measure. In this talk, we will introduce a new framework where the frequency and parameter interpolation points are selected jointly to minimize a global tensor $\mathcal{H} _ 2$-$L _ 2$ norm, $\mathcal{H} _ 2$ in the frequency, $L _ 2$ in the parameter domain. We will provide the first-order conditions in this $\mathcal{H} _ 2$-$L _ 2$ norm for an optimal parametric reduced model.