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On structure preserving model reduction for damped wave propagation in transport networks

Submission Status:under review
  • We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass, dissipation of energy, passivity, existence of steady states, and exponential stability can be preserved by an appropriate semi- discretization in space via a mixed finite element method and also during the further dimension reduction by structure preserving Galerkin projection which is the main focus of this paper. Krylov subspace methods are employed for the construction of the reduced models and we discuss modifications needed to satisfy certain algebraic compatibility conditions; these are required to ensure the well-posedness of the reduced models and the preservation of the key properties. Our analysis is based on the underlying infinite dimensional problem and its Galerkin approximations. The proposed algorithms therefore have a direct interpretation in function spaces; in principle, they are even applicable directly to the original system of partial differential-algebraic equations while the intermediate discretization by finite elements is only required for the actual computations. The performance of the proposed methods is illustrated with numerical tests and the necessity for the compatibility conditions is demonstrated by examples.

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Metadaten
Author:Herbert Egger, Thomas Kugler, Björn Liljegren-Sailer, Nicole Marheineke, Volker Mehrmann
Document Type:Preprint
Language:English
Date of Publication (online):2017/11/04
Date of first Publication:2017/07/20
Release Date:2017/07/20
Tag:Galerkin projection; partial differential-algebraic equations; port-Hamiltonian systems
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Technische Universität Darmstadt
Technische Universität Berlin
Subprojects:B03
C02
C04