Modern simulation scenarios require real-time or many query responses from a simulation model. This is the driving force for increased efforts in model order reduction for high dimensional dynamical systems or partial differential equations. This demand for fast simulation models is even more critical for parametrized problems. Several snapshot-based methods for basis construction exist for parametrized model order reduction, e.g. proper orthogonal decomposition (POD) or reduced basis (RB) methods. An often faced problem is that the produced reduced models for a given accuracy tolerance are still of too high dimension. This is especially the case for evolution problems where the model shows high variability during time evolution. We will present an approach to gain control over the online complexity of a reduced model by an adaptive time domain partitioning. Thereby we can prescribe simultaneously a desired error tolerance and a limiting size of the dimension of the reduced model. This leads to fast and accurate reduced models. The method will be applied to an advection problem.

@InProceedings{DDH11,
  author       = {Dihlmann, M. and Drohmann, M. and Haasdonk, B.},
  title        = {Model reduction of parametrized evolution problems using the reduced basis method with adaptive time partitioning},
  booktitle    = {International Conference on Adaptive Modeling and Simulation ADMOS 2011},
  year         = {2011},
  editor       = {D. Aubry and P. Diez },
  note         = {(submitted)},
  url          = \{/2011/DDH11},
}