Seminar in Numerical Analysis: Matthias Voigt (FernUni Schweiz)

Structure-Preserving Model Reduction for Symmetric Second-Order Systems

We introduce a model reduction approach for linear time-invariant second-order systems based on positive real balanced truncation.
Our method guarantees to preserve passivity of the reduced-order model as well as the positive definiteness of the mass and stiffness matrices and admits an a priori gap metric error bound.
Our construction of the second-order reduced model is based on the consideration of an internal symmetry structure and the invariant zeros of the system and their sign-characteristics for which we derive a normal form.
The results are available in [1].

[1] I. Dorschky, T. Reis, and M. Voigt. Balanced truncation model reduction for symmetric second order systems - a passivity-based approach. SIAM J. Matrix Anal. Appl., 42(4):1602--1635, 2021.

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