Browsing by Author "Grunert, Dennis"

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Open Access
A non-intrusive nonlinear model reduction method for structural dynamical problems based on machine learning
(2020) Kneifl, Jonas; Grunert, Dennis; Fehr, Jörg
The paper uses a nonlinear non-intrusive model reduction approach, to derive efficient and accurate surrogate models for structural dynamical problems. Therefore, a combination of proper orthogonal decomposition along with regression algorithms from the field of machine learning is utilized to capture the dynamics in a reduced representation. This allows highly performant approximations of the original system. In this context, we provide a comparison of several regression algorithms based on crash simulations of a structural dynamic frame.
Open Access
Well-scaled, a-posteriori error estimation for model order reduction of large second-order mechanical systems
(2019) Grunert, Dennis; Fehr, Jörg; Haasdonk, Bernard
Model Order Reduction is used to vastly speed up simulations but it also introduces an error to the simulation results, which needs to be controlled. The performance of the general to use, a-posteriori error estimator of Ruiner et al. for second-order systems is analyzed and a bottleneck is found in the offline stage making it unusable for larger models. We use the spectral theorem, power series expansions, monotonicity properties, and self-tailored algorithms to speed up the offline stage largely by one polynomial order both in terms of computation time as well as storage complexity. All properties are proven rigorously. This eliminates the aforementioned bottleneck. Hence, the error estimator of Ruiner et al. can finally be used for large, linear, second-order mechanical systems reduced by any model reduction method based on Petrov-Galerkin reduction. The examples show speedups of up to 28.000 and the ability to compute much larger systems with a fixed amount of memory.