Browsing by Author "Haasdonk, Bernard (Jun.-Prof. Dr.)"

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    Model reduction for nonlinear systems : kernel methods and error estimation
    (2013) Wirtz, Daniel; Haasdonk, Bernard (Jun.-Prof. Dr.)
    In this thesis we deal with model reduction for dynamical systems and multiscale models. Special emphasis are the application of kernel methods for nonlinear approximation and a-posteriori error estimation for reduced dynamical systems. The considered nonlinear approximation techniques comprise support vector machines, greedy-type vectorial algorithms and the DEIM along with some analysis. Those techniques are applied to provide approximations to nonlinear parts of dynamical systems that can be efficiently evaluated in the context of Galerkin projection based model reduction schemes. Furthermore, a-posteriori error estimation procedures are developed for both kernel-based and POD-DEIM reduced systems. In the context of multiscale model reduction, we show that the nonlinear approximation techniques introduced earlier can be successfully applied to provide cheap surrogate models for the micro scale.