Towards a Scalable Dynamic Spatial Database System

With the rise of GPS-enabled smartphones and other similar mobile devices, massive amounts of location data are available. However, no scalable solutions for soft real-time spatial queries on large sets of moving objects have yet emerged. In this paper we explore and measure the limits of actual algorithms and implementations regarding different application scenarios. And finally we propose a novel distributed architecture to solve the scalability issues.Comment: (2012

One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh

Novel approaches for constructing persistent Delaunay triangulations by applying different equations and different methods

“Delaunay triangulation and data structures are an essential field of study and research in computer science, for this reason, the correct choices, and an adequate design are essential for the development of algorithms for the efficient storage and/or retrieval of information. However, most structures are usually ephemeral, which means keeping all versions, in different copies, of the same data structure is expensive. The problem arises of developing data structures that are capable of maintaining different versions of themselves, minimizing the cost of memory, and keeping the performance of operations as close as possible to the original structure. Therefore, this research aims to aims to examine the feasibility concepts of Spatio-temporal structures such as persistence, to design a Delaunay triangulation algorithm so that it is possible to make queries and modifications at a certain time t, minimizing spatial and temporal complexity. Four new persistent data structures for Delaunay triangulation (Bowyer-Watson, Walk, Hybrid, and Graph) were proposed and developed. The results of using random images and vertex databases with different data (DAG and CGAL), proved that the data structure in its partial version is better than the other data structures that do not have persistence. Also, the full version data structures show an advance in the state of the technique. All the results will allow the algorithms to minimize the cost of memory”--Abstract, page iii

A parallel algorithm for Delaunay triangulation of moving points on the plane

Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very important in computational geometry for dealing with moving objects. However, when dealing with moving points, maintaining a dynamically changing Delaunay triangulation can be challenging. So, In this case, we have to update triangulation repeatedly. If points move so far, it is better to rebuild the triangulation. One approach to handle moving points is to use an incremental algorithm. For the case that points move slowly, we can give a faster algorithm than rebuilding it. Furthermore, sequential algorithms can be computationally expensive for large datasets. So, one way to compute as fast as possible is parallelism. In this paper, we propose a parallel algorithm for moving points. we propose an algorithm that divides datasets into equal partitions and give every partition to one block. Each block satisfay the Delaunay constraints after each time step and uses delete and insert algorithms to do this. We show this algorithm works faster than serial algorithms

JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi/Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a-priori bounds on element size and shape. Grid-quality is further improved through the application of hill-climbing type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution type studies is discussed in detail.Comment: Final revisions, as per: Engwirda, D.: JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere, Geosci. Model Dev., 10, 2117-2140, https://doi.org/10.5194/gmd-10-2117-2017, 201

Gap Processing for Adaptive Maximal Poisson-Disk Sampling

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201

The aerodynamic flow over a bluff body in ground proximity: CFD prediction of road vehicle aerodynamics using unstructured grids

The prediction of external automobile aerodynamics using Computational Fluid Dynamics (CFD) is still in its infancy. The restrictions on grid size for practical use limit the ability of most organisations to predict the full flow over an automobile. Some insight into the flow over a passenger car can be made by examining the flow over a bluff body in close proximity to the ground. One such body is the Ahmed body composed of a rounded front, straight mid-section and variable slant-rear section. This body exhibits many of the 3D flow structures exhibited by passenger cars. The main feature of the flow around this body is the change in flow structure as the angle of the slant surface at the rear of the body is increased. The flow starts fully attached and ends fully separated. In between these two regimes is a third high drag regime. The flow structure is characterised by strong counter-rotating longitudinal vortices originating from the interaction between the flow from the sides and top of the body, and a small separation from the top/slant edge on the centre-plane of the body. The flow reattaches to the slant surface and the low-pressure fluid within the separation bubble increases the drag considerably. The use of CFD incorporating tine averaged statistical turbulence models to reproduce these flow patterns is assessed in this study. Initial work concentrated on evaluating structured grid methods for this flow type. Some success was achieved with the flow fields for the attached and fully separated cases but the third high drag regime was not predicted. The flow field also exhibited a grid dependent flow structure and drag result. To examine these effects further without high grid overheads an unstructured mesh generator was developed and used to provide meshes with more grid cells clustered around the body and it's wake. Analysis and refinement of the unstructured grids proved successful at removing the grid dependent flow field but still showed no evidence of the third high drag flow regime. Further, the bulk levels of drag in all cases was too high and the fully separated flow regime occurred too late in the slant surface angle sweep, coming at 40° instead of the 30° seen in the wind tunnel results. Further analysis of the flow field using highly refined mixed meshes showed no improvement in the drag or flow field prediction with the high drag flow field still not present. The use of higher order differencing schemes and anisotropic turbulence models reduced the drag levels considerably but not to the levels seen in the wind tunnel results. Comparison of the results from this work with the work of other authors is difficult for two reasons. Firstly, work on the specific body used in this thesis is sparse and, secondly, much of the work done by other authors was in conjunction with automotive manufacturers and details of the specific numerical methods employed are not available. The most important parallel conclusion from the work presented here and that of other authors is the inability of the CFD prediction to capture the change in flow mode as the angle of slant surface is increased. This failure can, in all probability, be attributed to the use of a steady-state CFD solution algorithm to capture the flow field around the body. A small possibility perhaps still exists that further grid refinement, very localised around the body, would help, but the detailed and careful predictions presented in this study make this highly unlikely. The most important piece of further work that could follow this work would therefore be the application of a time-accurate (unsteady) CFD solution algorithm to the bluff body in ground proximity problem. Whether these predictions should be of an unsteady RANS nature, or full LES predictions would be best answered by applying these methods to the present flow problem which is fundamental to the study of automobile aerodynamics

A solution adaptive structured-unstructured grid procedure for unsteady flows

A solution adaptive hybrid grid method for the computation of two-dimensional, unsteady flows is presented. The method is capable of handling multiple component, complex geometries in relative motion, such as those encountered in turbomachinery analysis. The numerical approach uses a hybrid structured-unstructured zonal grid topology along with modeling equations and solution techniques that are most appropriate in the individual domains, thus combining the advantages of both structured and unstructured grid methods. The viscous flow region in the immediate vicinity of the airfoils is resolved using a third-order accurate, implicit, upwind solution of the Navier-Stokes equations on structured, O-type grids. Explicit solutions of the Euler equations are obtained in the rest of the domain that consists of an unstructured mesh made up of triangular cells. The use of both central- and upwind-differenced flux schemes is investigated for the unstructured domains. Methodologies for accurate, conservative transfer of information at the interface between the structured and unstructured domains as well as that between two unstructured grids in relative motion are developed. An efficient and robust solution adaptation strategy is developed which incorporates both refinement and de-refinement capabilities for the unstructured grid regions. Both time-averaged and time-resolved results are presented for test cases and are compared with available experimental data. The quality of the results obtained by the present method is comparable with those obtained by methods based on fully structured grids. Calculations performed using the solution adaptation capabilities are also presented

Finite Element Modeling Driven by Health Care and Aerospace Applications

This thesis concerns the development, analysis, and computer implementation of mesh generation algorithms encountered in finite element modeling in health care and aerospace. The finite element method can reduce a continuous system to a discrete idealization that can be solved in the same manner as a discrete system, provided the continuum is discretized into a finite number of simple geometric shapes (e.g., triangles in two dimensions or tetrahedrons in three dimensions). In health care, namely anatomic modeling, a discretization of the biological object is essential to compute tissue deformation for physics-based simulations. This thesis proposes an efficient procedure to convert 3-dimensional imaging data into adaptive lattice-based discretizations of well-shaped tetrahedra or mixed elements (i.e., tetrahedra, pentahedra and hexahedra). This method operates directly on segmented images, thus skipping a surface reconstruction that is required by traditional Computer-Aided Design (CAD)-based meshing techniques and is convoluted, especially in complex anatomic geometries. Our approach utilizes proper mesh gradation and tissue-specific multi-resolution, without sacrificing the fidelity and while maintaining a smooth surface to reflect a certain degree of visual reality. Image-to-mesh conversion can facilitate accurate computational modeling for biomechanical registration of Magnetic Resonance Imaging (MRI) in image-guided neurosurgery. Neuronavigation with deformable registration of preoperative MRI to intraoperative MRI allows the surgeon to view the location of surgical tools relative to the preoperative anatomical (MRI) or functional data (DT-MRI, fMRI), thereby avoiding damage to eloquent areas during tumor resection. This thesis presents a deformable registration framework that utilizes multi-tissue mesh adaptation to map preoperative MRI to intraoperative MRI of patients who have undergone a brain tumor resection. Our enhancements with mesh adaptation improve the accuracy of the registration by more than 5 times compared to rigid and traditional physics-based non-rigid registration, and by more than 4 times compared to publicly available B-Spline interpolation methods. The adaptive framework is parallelized for shared memory multiprocessor architectures. Performance analysis shows that this method could be applied, on average, in less than two minutes, achieving desirable speed for use in a clinical setting. The last part of this thesis focuses on finite element modeling of CAD data. This is an integral part of the design and optimization of components and assemblies in industry. We propose a new parallel mesh generator for efficient tetrahedralization of piecewise linear complex domains in aerospace. CAD-based meshing algorithms typically improve the shape of the elements in a post-processing step due to high complexity and cost of the operations involved. On the contrary, our method optimizes the shape of the elements throughout the generation process to obtain a maximum quality and utilizes high performance computing to reduce the overheads and improve end-user productivity. The proposed mesh generation technique is a combination of Advancing Front type point placement, direct point insertion, and parallel multi-threaded connectivity optimization schemes. The mesh optimization is based on a speculative (optimistic) approach that has been proven to perform well on hardware-shared memory. The experimental evaluation indicates that the high quality and performance attributes of this method see substantial improvement over existing state-of-the-art unstructured grid technology currently incorporated in several commercial systems. The proposed mesh generator will be part of an Extreme-Scale Anisotropic Mesh Generation Environment to meet industries expectations and NASA\u27s CFD visio