BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Philipp Schulze (TU Berlin) DTSTART:20241002T140000Z DTEND:20241002T150000Z DTSTAMP:20260423T023942Z UID:PHSeminar/8 DESCRIPTION:Title: Structure-Preserving Model Reduction for Dissipative and Port-Hamiltonia n Systems\nby Philipp Schulze (TU Berlin) as part of Port-Hamiltonian Seminar\n\n\nAbstract\nModel order reduction (MOR) is a powerful tool for reducing the computational effort in applications where a computational mo del needs to be evaluated multiple times\, e.g.\, in control and optimizat ion. MOR aims to replace the full-order model (FOM) by a reduced-order mod el (ROM) which should be cheap to evaluate and sufficiently accurate. In m any applications it is also desirable to preserve important properties of the FOM such as stability or passivity. One possibility to guarantee this preservation is to use MOR schemes which preserve a dissipative or port-Ha miltonian structure. While there are structure-preserving variants of the most common MOR techniques available\, these methods typically lack comput able a priori error bounds and suffer from a loss of accuracy in compariso n to their non-structure-preserving counterparts. Moreover\, these techniq ues are based on linear subspace approximations of the FOM state and such linear approaches usually perform poorly for transport-dominated systems.\ n\nIn the first part of this talk\, we present a structure-preserving bala ncing-based MOR approach which allows to provide computable a priori error bounds. Furthermore\, we demonstrate that the accuracy of the ROM may be significantly improved by replacing the FOM Hamiltonian by another one whi ch is based on an extremal solution of the corresponding Kalman-Yakubovich -Popov inequality. In the second part of this talk\, we address the questi on of how to construct structure-preserving MOR schemes when using a nonli near approximation ansatz\, which is especially relevant in the context of transport-dominated systems. For a special class of nonlinear ansatzes\, we demonstrate that structure-preserving ROMs may be obtained based on a w eighted residual minimization scheme. The effectiveness of the presented a pproaches is demonstrated by means of numerical examples.\n\nThe first par t of this talk is based on joint work with Tobias Breiten and Riccardo Mor andin.\n LOCATION:https://researchseminars.org/talk/PHSeminar/8/ END:VEVENT END:VCALENDAR