20170508
The basic idea of model order reduction utilizing proper orthogonal decomposition (PODMOR) consists in replacing a highdimensional problem by a lowdimensional POD approximation with the aim to save computational times and storage capacity while preserving a good approximation quality. Following the idea of Sirovich (1987), the POD surrogate models are built upon snapshot information which is retrieved from the underlying dynamical system. In this framework it is important to choose suitable time instances (snapshot locations). For this reason, in the first part of this talk an aposteriori error control strategy will be discussed which is based on a reformulation of the optimality system of the optimal control problem (adaptivity with respect to time). Finally, in many applications adaptive finite element methods are unavoidable in order to implement numerical simulations. In a fully discrete setting, this means that the snapshots are vectors of different lengths due to the different spatial resolutions at each time instance. In the second part of the talk, we will investigate an infinitedimensional approach in order to combine adaptive finite element methods with POD reduced order modeling (adaptivity with respect to space). Numerical examples will illustrate the presented methods.
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
Dolivostraße 15
D64293 Darmstadt

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