Efficient Reduced Models for Parametrized Dynamical Systems by Offline/online Decomposition

Reduced basis (RB) methods are effective methods for model reduction of parametrized partial differential equations (P2DEs). During the last years various types of stationary and timedependent, linear and nonlinear P2DEs have been treated. In the field of dynamical systems’ order reduction, these methods are largely unknown, but the interest in reduction of parametrized systems is increasing. In the current presentation, we show that some characteristic components of RB-methods can be transfered to model reduction of parametrized dynamical systems. We exemplify this for linear systems with output estimation. A so called offline/online decomposition is the key for efficient simulation: In the offline phase, one prepares the reduced basis and auxiliary parameter-independent quantities. These preparations allow rapid online simulations for varying parameters. The possibly extensive offline phase pays off in case of a multi-query context, where sufficiently many reduced simulations with different parameter constellations are to be expected. In addition to the effective reduced simulation schemes, error control is possible by a posteriori error estimators. These are based on residual analysis and can also be effectively decomposed in an offline/online fashion and hence allow fast and rigorous error guarantees.