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Auflistung nach Autor:in "Bobach, T."

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  • Textdokument
    Comparative tensor visualisation within the framework of consistent time-stepping schemes
    (Visualization of large and unstructured data sets, 2008) Mohr, R.; Bobach, T.; Hijazi, Y.; Reis, G.; Steinmann, P.; Hagen, H.
    Nowadays, the design of so-called consistent time-stepping schemes that basically feature a physically correct time integration, is still a state-of-the-art topic in the area of numerical mechanics. Within the proposed framework for finite elastoplasto-dynamics, the spatial as well as the time discretisation rely both on a Finite Element approach and the resulting algorithmic conservation properties have been shown to be closely related to quadrature formulas that are required for the calculation of time-integrals. Thereby, consistent integration schemes, which allow a superior numerical performance, have been developed based on the introduction of an enhanced algorithmic stress tensor, compare [MMS06]-[MMS07c]. In this contribution, the influence of this consistent stress enhancement, representing a modified time quadrature rule, is analysed for the first time based on the spatial distribution of the tensor-valued difference between the standard quadrature rule, relying on a specific evaluation of the well-known continuum stresses, and the favoured nonstandard quadrature rule, involving the mentioned enhanced algorithmic stresses. This comparative analysis is carried out using several visualisation tools tailored to set apart spatial and temporal patterns that allow to deduce the influence of both step size and material constants on the stress enhancement. The resulting visualisations indeed confirm the physical intuition by pointing out locations where interesting changes happen in the data.
  • Textdokument
    Natural neighbor concepts in scattered data interpolation and discrete function approx- imation
    (Visualization of large and unstructured data sets, 2008) Bobach, T.; Umlauf, G.
    The concept of natural neighbors employs the notion of distance to define local neighborhoods in discrete data. Especially when querying and accessing large scale data, it is important to limit the amount of data that has to be processed for an answer. Because of its implicit definition on distances, the natural neighbor concept is extremely well suited to provide meaningful neighborhoods in spatial data with a scattered, inhomogeneous distribution. This paper revisits some unique properties of natural neighbor based methods and summarizes important findings for their successful application to scattered data interpolation, and the computation of discrete harmonic functions.