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International Journal for Uncertainty Quantification

Impact factor: 0.967

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2015010171
pages 255-273

STOCHASTIC GALERKIN METHODS AND MODEL ORDER REDUCTION FOR LINEAR DYNAMICAL SYSTEMS

Roland Pulch
Department of Mathematics and Computer Science, Ernst-Moritz-Arndt-Universitat Greifswald, Walther-Rathenau-Strasse 47, D-17487 Greifswald, Germany
E. Jan W. ter Maten
Centre for Analysis, Scientific computing and Applications (CASA), Dept. Mathematics & Computer Science, Technische Universiteit Eindhoven, P.O.Box 513, NL-5600 MB Eindhoven, The Netherlands; Bergische Universitat Wuppertal, D-42119 Wuppertal, Germany

ABSTRACT

Linear dynamical systems are considered in the form of ordinary differential equations or differential algebraic equations. We change their physical parameters into random variables to represent uncertainties. A stochastic Galerkin method yields a larger linear dynamical system satisfied by an approximation of the random processes. If the original systems own a high dimensionality, then a model order reduction is required to decrease the complexity. We investigate two approaches: the system of the stochastic Galerkin scheme is reduced and, vice versa, the original systems are reduced followed by an application of the stochastic Galerkin method. The properties are analyzed in case of reductions based on moment matching with the Arnoldi algorithm. We present numerical computations for two test examples.