Synthesis of Frame Field-Aligned Multi-Laminar Structures

In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods because it can represent the microstructural design at a much finer length-scale than the computational grid. The optimal microstructure for a single load case is an orthogonal rank-3 laminate. A rank-3 laminate can be described in terms of frame fields, which are also an important tool for mesh generation in both 2D and 3D. We propose a method for generating multi-laminar structures from frame fields. Rather than relying on integrative approaches that find a parametrization based on the frame field, we find stream surfaces, represented as point clouds aligned with frame vectors, and we solve an optimization problem to find well-spaced collections of such stream surfaces. The stream surface tracing is unaffected by the presence of singularities outside the region of interest. Neither stream surface tracing nor selecting well-spaced surface rely on combed frame fields. In addition to stream surface tracing and selection, we provide two methods for generating structures from stream surface collections. One of these methods produces volumetric solids by summing basis functions associated with each point of the stream surface collection. The other method reinterprets point sampled stream surfaces as a spatial twist continuum and produces a hexahedralization by dualizing a graph representing the structure. We demonstrate our methods on several frame fields produced using the homogenization approach for topology optimization, boundary-aligned, algebraic frame fields, and frame fields computed from closed-form expressions.Comment: 19 pages, 18 figure

New techniques for the scientific visualization of three-dimensional multi-variate and vector fields

Volume rendering allows us to represent a density cloud with ideal properties (single scattering, no self-shadowing, etc.). Scientific visualization utilizes this technique by mapping an abstract variable or property in a computer simulation to a synthetic density cloud. This thesis extends volume rendering from its limitation of isotropic density clouds to anisotropic and/or noisy density clouds. Design aspects of these techniques are discussed that aid in the comprehension of scientific information. Anisotropic volume rendering is used to represent vector based quantities in scientific visualization. Velocity and vorticity in a fluid flow, electric and magnetic waves in an electromagnetic simulation, and blood flow within the body are examples of vector based information within a computer simulation or gathered from instrumentation. Understand these fields can be crucial to understanding the overall physics or physiology. Three techniques for representing three-dimensional vector fields are presented: Line Bundles, Textured Splats and Hair Splats. These techniques are aimed at providing a high-level (qualitative) overview of the flows, offering the user a substantial amount of information with a single image or animation. Non-homogenous volume rendering is used to represent multiple variables. Computer simulations can typically have over thirty variables, which describe properties whose understanding are useful to the scientist. Trying to understand each of these separately can be time consuming. Trying to understand any cause and effect relationships between different variables can be impossible. NoiseSplats is introduced to represent two or more properties in a single volume rendering of the data. This technique is also aimed at providing a qualitative overview of the flows

Visuelle Analyse großer Partikeldaten

Partikelsimulationen sind eine bewährte und weit verbreitete numerische Methode in der Forschung und Technik. Beispielsweise werden Partikelsimulationen zur Erforschung der Kraftstoffzerstäubung in Flugzeugturbinen eingesetzt. Auch die Entstehung des Universums wird durch die Simulation von dunkler Materiepartikeln untersucht. Die hierbei produzierten Datenmengen sind immens. So enthalten aktuelle Simulationen Billionen von Partikeln, die sich über die Zeit bewegen und miteinander interagieren. Die Visualisierung bietet ein großes Potenzial zur Exploration, Validation und Analyse wissenschaftlicher Datensätze sowie der zugrundeliegenden Modelle. Allerdings liegt der Fokus meist auf strukturierten Daten mit einer regulären Topologie. Im Gegensatz hierzu bewegen sich Partikel frei durch Raum und Zeit. Diese Betrachtungsweise ist aus der Physik als das lagrange Bezugssystem bekannt. Zwar können Partikel aus dem lagrangen in ein reguläres eulersches Bezugssystem, wie beispielsweise in ein uniformes Gitter, konvertiert werden. Dies ist bei einer großen Menge an Partikeln jedoch mit einem erheblichen Aufwand verbunden. Darüber hinaus führt diese Konversion meist zu einem Verlust der Präzision bei gleichzeitig erhöhtem Speicherverbrauch. Im Rahmen dieser Dissertation werde ich neue Visualisierungstechniken erforschen, welche speziell auf der lagrangen Sichtweise basieren. Diese ermöglichen eine effiziente und effektive visuelle Analyse großer Partikeldaten

Brain explorer for connectomic analysis

Visualization plays a vital role in the analysis of multimodal neuroimaging data. A major challenge in neuroimaging visualization is how to integrate structural, functional, and connectivity data to form a comprehensive visual context for data exploration, quality control, and hypothesis discovery. We develop a new integrated visualization solution for brain imaging data by combining scientific and information visualization techniques within the context of the same anatomical structure. In this paper, new surface texture techniques are developed to map non-spatial attributes onto both 3D brain surfaces and a planar volume map which is generated by the proposed volume rendering technique, spherical volume rendering. Two types of non-spatial information are represented: (1) time series data from resting-state functional MRI measuring brain activation; (2) network properties derived from structural connectivity data for different groups of subjects, which may help guide the detection of differentiation features. Through visual exploration, this integrated solution can help identify brain regions with highly correlated functional activations as well as their activation patterns. Visual detection of differentiation features can also potentially discover image-based phenotypic biomarkers for brain diseases

Experimental Investigation and Large-Eddy Simulation of the Turbulent Flow past a Smooth and Rigid Hemisphere

Computations carried out on the German Federal Top-Level Computer SuperMUC at LRZ Munich under the contract number pr84na.International audienceThe objective of the present paper is to provide a detailed experimental and numerical investigation on the turbulent flow past a hemispherical obstacle (diameter D). For this purpose, the bluff body is exposed to a thick turbulent boundary layer of the thickness δ = D/2 at Re = 50,000. In the experiment this boundary layer thickness is achieved by specific fences placed in the upstream region of the wind tunnel. A detailed measurement of the upstream flow conditions by laser-Doppler and hot-film probes allows to mimic the inflow conditions for the complementary large-eddy simulation of the flow field using a synthetic turbulence inflow generator. These clearly defined boundary and operating conditions are the prerequisites for a combined experimental and numerical investigation of the flow field relying on the laser-Doppler anemometry and a finite-volume Navier-Stokes solver for block-structured curvilinear grids. The results comprise an analysis on the unsteady flow features observed in the vicinity of the hemisphere as well as a detailed discussion of the time-averaged flow field. The latter includes the mean velocity field as well as the Reynolds stresses. Owing to the proper description of the oncoming flow and supplementary numerical studies guaranteeing the choice of an appropriate grid and subgrid-scale model, the results of the measurements and the prediction are found to be in close agreement