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:20260513T213516Z 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 (pH Seminar)\n\n\nAbstract\nModel order reduction (MOR) is a power ful tool for reducing the computational effort in applications where a com putational model needs to be evaluated multiple times\, e.g.\, in control and optimization. MOR aims to replace the full-order model (FOM) by a redu ced-order model (ROM) which should be cheap to evaluate and sufficiently a ccurate. In many applications it is also desirable to preserve important p roperties of the FOM such as stability or passivity. One possibility to gu arantee this preservation is to use MOR schemes which preserve a dissipati ve or port-Hamiltonian structure. While there are structure-preserving var iants of the most common MOR techniques available\, these methods typicall y lack computable a priori error bounds and suffer from a loss of accuracy in comparison to their non-structure-preserving counterparts. Moreover\, these techniques are based on linear subspace approximations of the FOM st ate and such linear approaches usually perform poorly for transport-domina ted systems.\n\nIn the first part of this talk\, we present a structure-pr eserving balancing-based MOR approach which allows to provide computable a priori error bounds. Furthermore\, we demonstrate that the accuracy of th e ROM may be significantly improved by replacing the FOM Hamiltonian by an other one which is based on an extremal solution of the corresponding Kalm an-Yakubovich-Popov inequality. In the second part of this talk\, we addre ss the question of how to construct structure-preserving MOR schemes when using a nonlinear approximation ansatz\, which is especially relevant in t he context of transport-dominated systems. For a special class of nonlinea r ansatzes\, we demonstrate that structure-preserving ROMs may be obtained based on a weighted residual minimization scheme. The effectiveness of th e presented approaches is demonstrated by means of numerical examples.\n\n The first part of this talk is based on joint work with Tobias Breiten and Riccardo Morandin.\n LOCATION:https://researchseminars.org/talk/PHSeminar/8/ END:VEVENT END:VCALENDAR