11 Interfakultäre Einrichtungen

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/12

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Institute: search.filters.UBSInstitut.Stuttgarter Zentrum für Simulationswissenschaften (SC SimTech)Author: search.filters.author.Unger, Benjamin

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    Identification of linear time-invariant systems with dynamic mode decomposition
    (2022) Heiland, Jan; Unger, Benjamin
    Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge–Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge–Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.
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    Higher-order iterative decoupling for poroelasticity
    (2024) Altmann, Robert; Mujahid, Abdullah; Unger, Benjamin
    For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As the main result, we show that the convergence depends on the interplay between the time step size and the parameters for the contraction of the iterative scheme. Moreover, this connection is quantified explicitly, which allows for balancing the single error components. Several numerical experiments illustrate and validate the theoretical results, including a three-dimensional example from biomechanics.