07 Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/8

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    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.
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    Port-Hamiltonian fluid-structure interaction modelling and structure-preserving model order reduction of a classical guitar
    (2023) Rettberg, Johannes; Wittwar, Dominik; Buchfink, Patrick; Brauchler, Alexander; Ziegler, Pascal; Fehr, Jörg; Haasdonk, Bernard
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    Efficient parametric analysis of the chemical master equation through model order reduction
    (2012) Waldherr, Steffen; Haasdonk, Bernard
    BACKGROUND: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation.RESULTS:In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. CONCLUSIONS: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.