Visitation Graphs: Interactive Ensemble Visualization with Visitation Maps

Modern applications in computational science are increasingly focusing on understanding uncertainty in models and parameters in simulations. In this paper, we describe visitation graphs, a novel approximation technique for the well-established visualization of steady 2D vector field ensembles using visitation maps. Our method allows the efficient and robust computation of arbitrary visitation maps for vector field ensembles. A pre-processing step that can be parallelized to a high degree eschews the needs to store every ensemble member and to re-calculate every time the start position of the visitation map is changed. Tradeoffs between accuracy of generated visitation maps on one side and pre-processing time and storage requirements on the other side can be made. Instead of downsampling ensemble members to a storable size, coarse visitation graphs can be stored, giving more accurate visitation maps while still reducing the amount of data. Thus accurate visitation map creation is possible for ensembles where the traditional visitation map creation is prohibitive. We describe our approach in detail and demonstrate its effectiveness and utility on examples from Computational Fluid Dynamics

DESIGN AND IMPLEMENTATION OF INFORMATION PATHS IN DENSE WIRELESS SENSOR NETWORKS

In large-scale sensor networks with monitoring applications, sensor nodes are responsible to send periodic reports to the destination which is located far away from the area to be monitored. We model this area (referred to as the distributed source) with a positive load density function which determines the total rate of traffic generated inside any closed contour within the area. With tight limitations in energy consumption of wireless sensors and the many-to-one nature of communications in wireless sensor networks, the traditional definition of connectivity in graph theory does not seem to be sufficient to satisfy the requirements of sensor networks. In this work, a new notion of connectivity (called implementability) is defined which represents the ability of sensor nodes to relay traffic along a given direction field, referred to as information flow vector field $\vec{D}$. The magnitude of information flow is proportional to the traffic flux (per unit length) passing through any point in the network, and its direction is toward the flow of traffic. The flow field may be obtained from engineering knowledge or as a solution to an optimization problem. In either case, information flow flux lines represent a set of abstract paths (not constrained by the actual location of sensor nodes) which can be used for data transmission to the destination. In this work, we present conditions to be placed on $\vec{D}$ such that the resulting optimal vector field generates a desirable set of paths. In a sensor network with a given irrotational flow field $\vec{D}(x,y)$, we show that a density of $n(x,y)=O(|\vec{D}(x,y)|^2)$ sensor nodes is not sufficient to implement the flow field as $|\vec{D}|$ scales linearly to infinity. On the other hand, by increasing the density of wireless nodes to $n(x,y)=O(|\vec{D}(x,y)|^2 \log |\vec{D}(x,y)|)$, the flow field becomes implementable. Implementability requires more nodes than simple connectivity. However, results on connectivity are based on the implicit assumption of exhaustively searching all possible routes which contradicts the tight limitation of energy in sensor networks. We propose a joint MAC and routing protocol to forward traffic along the flow field. The proposed tier-based scheme can be further exploited to build lightweight protocol stacks which meet the specific requirements of dense sensor networks. We also investigate buffer scalability of sensor nodes routing along flux lines of a given irrotational vector field, and show that nodes distributed according to the sufficient bound provided above can relay traffic from the source to the destination with sensor nodes having limited buffer space. This is particularly interesting for dense wireless sensor networks where nodes are assumed to have very limited resources

Numerical simulation of non-Newtonian fluid flow in mixing geometries

In this thesis, a theoretical investigation is undertaken into fluid and mixing flows generated by various geometries for Newtonian and non-Newtonian fluids, on both sequential and parallel computer systems. The thesis begins by giving the necessary background to the mixing process and a summary of the fundamental characteristics of parallel architecture machines. This is followed by a literature review which covers accomplished work in mixing flows, numerical methods employed to simulate fluid mechanics problems and also a review of relevant parallel algorithms. Next, an overview is given of the numerical methods that have been reviewed, discussing the advantages and disadvantages of the different methods. In the first section of the work the implementation of the primitive variable finite element method to solve a simple two dimensional fluid flow problem is studied. For the same geometry colour band mixing is also investigated. Further investigational work is undertaken into the flows generated by various rotors for both Newtonian and non-Newtonian fluids. An extended version of the primitive variable formulation is employed, colour band mixing is also carried out on two of these geometries. The latter work is carried out on a parallel architecture machine. The design specifications of a parallel algorithm for a MIMD system are discussed, with particular emphasis placed on frontal and multifrontal methods. This is followed by an explanation of the implementation of the proposed parallel algorithm, applied to the same fluid flow problems as considered earlier and a discussion of the efficiency of the system is given. Finally, a discussion of the conclusions of the entire accomplished work is presented. A number of suggestions for future work are also given. Three published papers relating to the work carried out on the transputer networks are included in the appendices

General Purpose Flow Visualization at the Exascale

Exascale computing, i.e., supercomputers that can perform 1018 math operations per second, provide significant opportunity for improving the computational sciences. That said, these machines can be difficult to use efficiently, due to their massive parallelism, due to the use of accelerators, and due to the diversity of accelerators used. All areas of the computational science stack need to be reconsidered to address these problems. With this dissertation, we consider flow visualization, which is critical for analyzing vector field data from simulations. We specifically consider flow visualization techniques that use particle advection, i.e., tracing particle trajectories, which presents performance and implementation challenges. The dissertation makes four primary contributions. First, it synthesizes previous work on particle advection performance and introduces a high-level analytical cost model. Second, it proposes an approach for performance portability across accelerators. Third, it studies expected speedups based on using accelerators, including the importance of factors such as duration, particle count, data set, and others. Finally, it proposes an exascale-capable particle advection system that addresses diversity in many dimensions, including accelerator type, parallelism approach, analysis use case, underlying vector field, and more