Doctor of Philosophy

dissertationHigh-order finite element methods, using either the continuous or discontinuous Galerkin formulation, are becoming more popular in fields such as fluid mechanics, solid mechanics and computational electromagnetics. While the use of these methods is becoming increasingly common, there has not been a corresponding increase in the availability and use of visualization methods and software that are capable of displaying visualizations of these volumes both accurately and interactively. A fundamental problem with the majority of existing visualization techniques is that they do not understand nor respect the structure of a high-order field, leading to visualization error. Visualizations of high-order fields are generally created by first approximating the field with low-order primitives and then generating the visualization using traditional methods based on linear interpolation. The approximation step introduces error into the visualization pipeline, which requires the user to balance the competing goals of image quality, interactivity and resource consumption. In practice, visualizations performed this way are often either undersampled, leading to visualization error, or oversampled, leading to unnecessary computational effort and resource consumption. Without an understanding of the sources of error, the simulation scientist is unable to determine if artifacts in the image are due to visualization error, insufficient mesh resolution, or a failure in the underlying simulation. This uncertainty makes it difficult for the scientists to make judgments based on the visualization, as judgments made on the assumption that artifacts are a result of visualization error when they are actually a more fundamental problem can lead to poor decision-making. This dissertation presents new visualization algorithms that use the high-order data in its native state, using the knowledge of the structure and mathematical properties of these fields to create accurate images interactively, while avoiding the error introduced by representing the fields with low-order approximations. First, a new algorithm for cut-surfaces is presented, specifically the accurate depiction of colormaps and contour lines on arbitrarily complex cut-surfaces. Second, a mathematical analysis of the evaluation of the volume rendering integral through a high-order field is presented, as well as an algorithm that uses this analysis to create accurate volume renderings. Finally, a new software system, the Element Visualizer (ElVis), is presented, which combines the ideas and algorithms created in this dissertation in a single software package that can be used by simulation scientists to create accurate visualizations. This system was developed and tested with the assistance of the ProjectX simulation team. The utility of our algorithms and visualization system are then demonstrated with examples from several high-order fluid flow simulations

GPU-based volume visualization from high-order finite element fields

pre-printThis paper describes a new volume rendering system for spectral/hp finite-element methods that has as its goal to be both accurate and interactive. Even though high-order finite element methods are commonly used by scientists and engineers, there are few visualization methods designed to display this data directly. Consequently, visualizations of high-order data are generally created by first sampling the high-order field onto a regular grid and then generating the visualization via traditional methods based on linear interpolation. This approach, however, introduces error into the visualization pipeline and requires the user to balance image quality, interactivity, and resource consumption. We first show that evaluation of the volume rendering integral, when applied to the composition of piecewise-smooth transfer functions with the high-order scalar field, typically exhibits second-order convergence for a wide range of high-order quadrature schemes, and has worst case first-order convergence. This result provides bounds on the ability to achieve high-order convergence to the volume rendering integral. We then develop an algorithm for optimized evaluation of the volume rendering integral, based on the categorization of each ray according to the local behavior of the field and transfer function. We demonstrate the effectiveness of our system by running performance benchmarks on several high-order fluid-flow simulations

ElVis: A system for the accurate and interactive visualization of high-order finite element solutions

pre-printThis paper presents the Element Visualizer (ElVis), a new, open-source scientific visualization system for use with high order finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these types of fields by querying the underlying finite element basis functions (e.g., high-order polynomials) directly, leading to pixel-exact representations of solutions and geometry. The system interacts with simulation data through run time plugins, which only require users to implement a handful of operations fundamental to finite element solvers. The data in turn can be visualized through the use of cut surfaces, contours, isosurfaces, and volume rendering. These visualization algorithms are implemented using NVIDIA's OptiX GPU-based ray-tracing engine, which provides accelerated ray traversal of the high-order geometry, and CUDA, which allows for effective parallel evaluation of the visualization algorithms. The direct interface between ElVis and the underlying data differentiates it from existing visualization tools. Current tools assume the underlying data is composed of linear primitives; high-order data must be interpolated with linear functions as a result. In this work, examples drawn from aerodynamic simulations-high-order discontinuous Galerkin finite element solutions of aerodynamic flows in particular-will demonstrate the superiority of ElVis' pixel-exact approach when compared with traditional linear-interpolation methods. Such methods can introduce a number of inaccuracies in the resulting visualization, making it unclear if visual artifacts are genuine to the solution data or if these artifacts are the result of interpolation errors. Linear methods additionally cannot properly visualize curved geometries (elements or boundaries) which can greatly inhibit developers' debugging efforts. As we will show, pixel-exact visualization exhibits none of these issues, removing the visualization scheme as a source of uncertainty for engineers using ElVis

Virtual Patching: Fighting Brute Force Attacks in a Software Defined Network

A new design for virtual patching applications is presented for software defined network environments. Based on OpenFlow implementation, a software defined network can be programmed to intelligently detect threats and handle them accordingly. By implementing a virtual patching solution with the Floodlight OpenFlow API, these networks can detect malicious traffic before it reaches the vulnerable device, based on common signs like packet size or destinations of open but unused ports. A controller hosts an Intrusion Detection Service (IDS) on the network would track signs of malicious data, and scan incoming traffic for any of those signs. If a packet is reasonably suspicious, it is not allowed to continue on it’s path, while all other traffic continues as normal. Because software defined networks are inherently programmable, a general solution can be put in place that network administrators can use to create virtual patching rules on the fly. This allows for vast flexibility and efficiency, which is critical when dealing with a live exploitation on the network. Experimental results for both the attack specific solution and the general, programmable solution have not yet been obtained

Math in Motion

Everything we know about the universe rests on the foundation of mathematics. Somehow, though, the magic of mathematics – the true power of numbers and their beautiful wildness – gets lost in math class. Children, our most magical thinkers, get turned off math in grade school and miss out on a language through which they could learn to read and change the world. VCU Math In Motion will generate a creative, dynamic STEM education initiative within the Richmond community using an innovative curriculum and a customized mobile unit to bring the beauty of math to Richmond region school children in grades 5-9, through partnerships across VCU and within the local school system

Impact of periodontal intervention on local inflammation, periodontitis, and HIV outcomes

Periodontal disease resolution was hypothesized to impact systemic HIV measures

Predictors of New-Onset Atrial Fibrillation in Geriatric Trauma Patients

Geriatric patients (age \u3e65) comprise a growing segment of the trauma population. New-onset atrial fibrillation may occur after injury, complicating clinical management and resulting in significant morbidity and mortality. This study was undertaken to identify clinical and demographic factors associated with new-onset atrial fibrillation among geriatric trauma patients . Methods: In this case control study, eligible participants included admitted trauma patients age 65 and older who developed new-onset atrial fibrillation during the hospitalization. Controls were admitted trauma patients who were matched for age and injury severity score, who did not develop atrial fibrillation. We evaluated the associations between new-onset atrial fibrillation and clinical characteristics, including patient demographics, health behaviors, chronic medical conditions, and course of care. Results: Data were available for 63 cases and 25 controls. Patients who developed atrial fibrillation were more likely to be male, compared to controls (49% versus 24%; odds ratio 3.0[1.0, 8.9]). Other demographic and clinical factors were not associated with new-onset atrial fibrillation, including mechanism of injury, co-morbid medical conditions, drug or alcohol use, surgical procedures, and intravenous fluid administration. Conclusions: Male geriatric trauma patients were at higher risk for developing new-onset atrial fibrillation. Other demographic and clinical factors were not associated with new-onset atrial fibrillation. Competing Interests: The authors report no conflicts of interest