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Model order reduction for networks of ODE and PDE systems. (English) Zbl 1266.93017
Hömberg, Dietmar (ed.) et al., System modeling and optimization. 25th IFIP TC 7 conference on system modeling and optimization, CSMO 2011, Berlin, Germany, September 12–16, 2011. Revised Selected Papers. Heidelberg: Springer (ISBN 978-3-642-36061-9/hbk; 978-3-642-36062-6/ebook). IFIP Advances in Information and Communication Technology 391, 92-101 (2013).
Summary: We propose a model order reduction (MOR) approach for networks containing simple and complex components. Simple components are modeled by linear ODE (and/or DAE) systems, while complex components are modeled by nonlinear PDE (and/or PDAE) systems. These systems are coupled through the network topology using the Kirchhoff laws. As application we consider MOR for electrical networks, where semiconductors form the complex components which are modeled by the transient drift-diffusion equations (DDEs). We sketch how proper orthogonal decomposition (POD) combined with discrete empirical interpolation (DEIM) and passivity-preserving balanced truncation methods for electrical circuits (PABTEC) can be used to reduce the dimension of the model. Furthermore we investigate residual-based sampling to construct reduced order models which are valid over a certain parameter range.
For the entire collection see [Zbl 1262.00009].

MSC:
93A30 Mathematical modelling of systems (MSC2010)
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65B99 Acceleration of convergence in numerical analysis
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