S07 - Visualisation of Large and Unstructured Data Sets
Visualisation of Large and Unstructured Data Sets
Hans Hagen, Martin Hering-Bertram, Christoph Garth (Eds.)
GI-Edition - Lecture Notes in Informatics (LNI), S-7
Bonner Köllen Verlag 2007
ISSN 1614-3213
ISBN 3-88579-441-7
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- TextdokumentComparative 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.
- TextdokumentDeriving global material properties of a microscopically heterogeneous medium - computational homogenisation and opportunities in visualisation(Visualization of large and unstructured data sets, 2008) Hirschberger, C. B.; Ricker, S.; Steinmann, P.; Sukumar, N.In order to derive the overall mechanical response of a microscopically material body, both the theoretical and the numerical framework of multi scale consideration coined as computational homogenisation is presented. Instead of resolving the actual heterogeneous microstructure in all detail for its simulation, representative micro elements are considered which provide the material properties for the coarse or rather scale. This procedure allows for a smaller and less inexpensive computation. However both the chance and challenge of visualising the decisive features arise on two scales.
- TextdokumentFinite elasto-plasto-dynamics a challenges & solutions(Visualization of large and unstructured data sets, 2008) Mohr, R.; Menzel, A.; Steinmann, P.In this contribution, we deal with time-stepping schemes for geometrically nonlinear multiplicative elasto-plasto-dynamics. Thereby, the approximation in space as well as in time rely both on a Finite Element approach, providing a general framework which conceptually includes also higher-order schemes. In this context, the algorithmic conservation properties of the related integrators strongly depend on the numerical computation of time integrals, particularly, if plastic deformations are involved. However, the application of adequate quadrature rules enables a fulfilment of physically motivated balance laws and, consequently, the consistent integration of finite elasto-plasto-dynamics. Using exemplarily linear Finite Elements in time, the resulting integration schemes are analysed regarding the obtained conservation properties and assessed in comparison to classical time-stepping schemes which commonly adopt a time-discretisation procedure based on Finite Differences. 88 On the one hand, computational modelling of materials and structures often demands the incorporation of inelastic and dynamic effects. On the other hand, the performance of classical time integration schemes for structural dynamics, as for instance developed in [HHT77, New59], is strongly restricted when dealing with highly nonlinear systems. In a nonlinear setting, advanced numerical techniques are required to satisfy the classical balance laws as for instance balance of linear and angular momentum or the classical laws of thermodynamics. Nowadays, energy and momentum conserving time integrators for dynamical systems, like multibody systems or elasto-dynamics, are well-established in the computational dynamics community, compare e.g. [BB99, BBT01a, BBT01b, Gonz00, KC99, ST92]. In contrast to the commonly used time discretisation based on Finite Differences, one-step implicit integration algorithms relying on Finite Elements in space and time were developed, for instance, in Betsch and Steinmann [BS00a, BS00b, BS01]. Therein, conservation of energy and angular momentum have been shown to be closely related to quadrature formulas required for numerical integration in time. Furthermore, specific algorithmic energy conserving schemes for hyperelastic materials can be based on the introduction of an enhanced stress tensor for time shape functions of arbitrary order, compare Gross et al. [GBS05]. However, most of the proposed approaches are restricted to conservative dynamical systems. Nevertheless, the consideration of plastic deformations in a dynamical framework, involving dissipation effects, is of cardinal importance for various applications in engineering. In the last years, notable contributions dealing with finite elasto-plasto-dynamics have been published by Meng and Laursen [ML02a, ML02b], Noels et al. [NSP06] and Armero [Arm05, Arm06, AZ06]. In this contribution, we follow the concepts which have been proposed for hyperelasticity in [BS01, GBS05] and pickup the general framework of Galerkin methods in space and time, developing integrators for finite multiplicative elasto-plasto-dynamics with pre-defined conservation properties, compare Mohr et al. [MMS06a, MMS07c, MMS07a, MMS07b]. By means of a representative numerical example, the excellent performance of the resulting schemes, which base on linear Finite Elements in time combined with different quadrature rules, will be demonstrated and compared with the performance of well-accepted standard integrators. 2 Semi-Discrete Dynamics To set the stage, we start with some basic notation of geometrically nonlinear continuum mechanics. First, the nonlinear deformation map $φ$(X, t) : B0 $\times $[0, T ] $\rightarrow $Bt shall be
- TextdokumentA framework for the visualization of brain structures(Visualization of large and unstructured data sets, 2008) Thelen, S.; Bierz, T.; Müller, B.; Hagen, Hans; Ebert, A.; Friauf, E.; Meyer, J.Nowadays biologists investigate different causes for deafness. One reason is a damage in a particular region of the auditory brain stem. Anatomical differences were discovered when investigating brain slices of different laboratory mice. However, these slices are only a two dimensional representation of a part of the brain. The arising question was how these differences of structure affect the three dimensional representation of this region. Therefore, an interdisciplinary framework was developed, which allows even unexperienced users to investigate and compare these regions.
- TextdokumentA framework for visualizing multivariate geodata(Visualization of large and unstructured data sets, 2008) Middel, A.In urban planning, sophisticated simulation models are key tools to estimate future population growth for measuring the impact of planning decisions on urban developments and the environment. Simulated population projections usually result in bulky, large-scale, multivariate geospatial data sets. Millions of records have to be processed, stored, and visualized to help planners explore and analyze complex population patterns. This paper introduces a database driven framework for visualizing geospatial multivariate simulation data from UrbanSim, a software-based simulation model for the analysis and planning of urban developments. The designed framework is extendable and aims at integrating methods from information visualization and cartography into planning processes.
- TextdokumentFrontmatter(Visualization of large and unstructured data sets, 2008)
- TextdokumentGeometric numerical integration of simple dynamical systems(Visualization of large and unstructured data sets, 2008) Schmitt, P. R.; Steinmann, P.Understanding the behavior of a dynamical system is usually accomplished by visualization of its phase space portraits. Finite element simulations of dynamical systems yield a very high dimensionality of phase space, i.e. twice the number of nodal degrees of freedom. Therefore insight into phase space structure can only be gained by reduction of the model's dimensionality. The phase space of Hamiltonian systems is of particular interest because of its inherent geometric features namely being the co-tangent bundle of the configuration space of the problem and therefore having a natural symplectic structure. In this contribution a class of geometry preserving integrators based on Lie-groups and -algebras is presented which preserve these geometric features exactly. Examples of calculations for a simple dynamical system are detailed.
- TextdokumentGeomodeling and Geovisualizations in Urban Planning und Real Estate Industry: The Example of Office Market Research(Visualization of large and unstructured data sets, 2008) von Malottki, C.Modeling, quantitative analysis, and forecasting in urban planning have a tradition since the sixties when very complex models for the whole “system of the city” were developed. After a phase of criticism about these complex black box programs in the eighties the topic got in the research focus again because of the easier possibilities for visualizing the results by the means of GIS. Subsequently, geomodeling is also interesting for more specific questions. The example shown in the paper is office market modeling – with a case study in Stuttgart. Due to higher vacancy rates and the degradation of buildings especially from the sixties and the seventies the subject is relevant for investors and real estate brokers but also for city administrations who try to avoid the degradation of whole areas. The classical time-series based office market models from urban economics describe the movement of the entire market but they do not consider local heterogeneity. Cross- sectional models like hedonic price modeling and an adaptation of the hedonic model for vacancy rates shown in the paper are difficult to couple with forecasting results. The microsimulation approach is the best way to integrate forecasting and a detailed spatial resolution. It consists in simulating movements, location choices, and vacancy at the building level. The paper presents the equations and exemplary results of the different simulation steps.
- TextdokumentGPU accelerated gesture detection for real time interaction(Visualization of large and unstructured data sets, 2008) Bierz, T.; Ebert, A.; Meyer, J.Over the past years, the interaction between humans and computers (HCI) evolved to one of the most important research topics in computer science. Therefore, finding a way for an intuitive, easy and affordable interaction is the main challenge. Optical markerless tracking using consumer hardware can satisfy these problems. However, in order to be able to interact in an efficient way, the tracking and furthermore the interaction must be handled in real time. This leads to efficient use of current GPUs in order to speed up the tracking and furthermore the gesture recognition. Involving these issues, an approach for an implementation and system will be presented in the following paper.
- TextdokumentNatural 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.