13 Zentrale Universitätseinrichtungen

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/14

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Institute: search.filters.UBSInstitut.Fakultätsübergreifend / Sonstige EinrichtungSubject: search.filters.subject.510

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    Local bilinear computation of Jacobi sets
    (2022) Klötzl, Daniel; Krake, Tim; Zhou, Youjia; Hotz, Ingrid; Wang, Bei; Weiskopf, Daniel
    We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.
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    Showpieces : scientific collections of the University of Stuttgart
    (Stuttgart : University of Stuttgart, 2023) Wiatrowski, Frank (Design, Photographs); Engstler, Katja Stefanie (Design); Ceranski, Beate (Preface); Rambach, Christiane (Preface)
    The university's scientific collections bear witness to a long tradition of teaching and research. The faculties and institutes, the university library and the university archives are home to diverse collections, some of which contain unusual or even unique objects. This brochure provides an initial insight into this often hidden world of university collections in Stuttgart.
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    Schaustücke : Einblicke in wissenschaftliche Sammlungen der Universität Stuttgart
    (Stuttgart : Universität Stuttgart, 2022) Wiatrowski, Frank (Gestaltung, Fotograf); Engstler, Katja Stefanie (Gestaltung); Ceranski, Beate (Vorwort); Rambach, Christiane (Vorwort)
    Die wissenschaftlichen Sammlungen der Universität zeugen von einer langen Lehr- und Forschungstradition. In Fakultäten und Instituten, in der Universitätsbibliothek und im Universitätsarchiv sind vielfältige Sammlungen beheimatet, zum Teil mit ungewöhnlichen oder gar einzigartigen Objekten. Die Broschüre gibt erste Einblicke in diese vielfach versteckte Welt der universitären Sammlungen in Stuttgart.
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    Fourth-order paired-explicit Runge-Kutta methods
    (2025) Doehring, Daniel; Christmann, Lars; Schlottke-Lakemper, Michael; Gassner, Gregor; Torrilhon, Manuel
    In this paper, we extend the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et al. (J Comput Phys 393:465-483, 2019) and Nasab and Vermeire (J Comput Phys 468:111470, 2022) to fourth-order of consistency. Based on the order conditions for partitioned Runge-Kutta methods we motivate a specific form of the Butcher arrays which leads to a family of fourth-order accurate methods. The employed form of the Butcher arrays results in a special structure of the stability polynomials, which needs to be adhered to for an efficient optimization of the domain of absolute stability. We demonstrate that the constructed fourth-order P-ERK methods satisfy linear stability, internal consistency, designed order of convergence, and conservation of linear invariants. At the same time, these schemes are seamlessly coupled for codes employing a method-of-lines approach, in particular without any modifications of the spatial discretization. We demonstrate speedup for single-threaded program executions, shared-memory parallelism, i.e., multi-threaded executions and distributed-memory parallelism with MPI. We apply the multirate P-ERK schemes to inviscid and viscous problems with locally varying wave speeds, which may be induced by non-uniform grids or multiscale properties of the governing partial differential equation. Compared to state-of-the-art optimized standalone methods, the multirate P-ERK schemes allow significant reductions in right-hand-side evaluations and wall-clock time, ranging from up to factors greater than four. A reproducibility repository is provided which enables the reader to examine all results presented in this work.