▼ This research presents a unique new software framework for representing and manipulating unstructured meshes in parallel, for use in modern scientific simulation codes. Due to the central nature of the unstructured mesh, this framework provides a variety of functionality, desirable throughout the lifecycle of an application, such as IO, parallel partitioning, phantom node data updates, adaptive refinement, derefinement and load balancing. What makes the framework unique is a focus on generality: like a database, the user provides a programmatic schema defining the structure of the mesh, including topological descriptions of the valid mesh entities. The system extracts adjacency information from this input and allows the use of high-level queries for manipulating and processing the mesh. Advanced C++ techniques allow for a combination of high extensibility and highly optimizable code. New applications can be built quickly, by taking advantage of the framework’s capabilities. Existing codes can incorporate the framework with minimal modification, due to the use of data proxies that mediate between the framework’s internal data structures and existing user data. The design and implementation of this framework are discussed, and several representative applications are presented. Scalability results and analysis are included. Advisors/Committee Members: Anderson, William K., Karman, Steve, Kapadia, Sagar, Matthews, John, College of Engineering and Computer Science.

▼ Computational simulation pervades science and engineering, enabling new insights about complex physical phenomena. The advent of exascale computer systems, which will enable simulation at an even greater scale, poses new challenges, motivating methods to cope with vastly increased amounts of simulation data. Enter data compression and reduction. Of particular interest are multilevel and hierarchical reduction methods, which split input data into a sequence of components tailored to the heterogeneous storage media of modern machines. Such methods are especially appropriate when the applications for which the data are to be used require varying levels of resolution. For instance, one user might require that the reduced dataset meet a prescribed error tolerance for the calculation of some derived quantity, while another might need it to fit in the available RAM for a responsive visualization. The first topic of this dissertation is the analysis of a simple lossless compression method based on decimation. Bounds on the expected compression ratio are derived and numerical illustrations of the performance of the technique are presented. The remainder of the dissertation is devoted to a suite of multilevel adaptive techniques inspired by the orthogonal and hierarchical decompositions. First, univariate algorithms for the two use cases of constrained loss and constrained storage are designed. Next, the technique is extended to the multivariate setting, and a loss estimator permitting the control of pointwise errors is introduced. Finally, a related loss estimator for Sobolev norms is used to perform reduction while limiting distortion in quantities of interest. Advisors/Committee Members: Ainsworth, Mark (Advisor), Darbon, Jérôme (Reader), Klasky, Scott (Reader).

▼ Many scientific simulations rely on the solution of very large linear systems of equations, and multigrid and domain decomposition methods are widely used solvers. It is unclear whether or not existing implementations of these methods will continue to perform in the same way on the next generation of supercomputers. In the first part, we study the impact of faults on the convergence of iterative solvers. We describe the different categories of faults and how they may be modeled using random matrices. Theoretical results concerning products of random matrices are given. We apply this novel theoretical framework to a two grid method, and extend the obtained convergence bounds to the multi-level case. It will transpire that multigrid in the presence of a fixed fault level will degenerate as the problem size grows. By protecting one of its steps, the prolongation operation, fault resilience is achieved. Practical details concerning the detection and mitigation of faults are discussed in order to leverage the theoretical results to obtain a fault-tolerant multigrid implementation. Finally, we extend the framework to cover faults in overlapping domain decomposition solvers. In the second part, we turn our attention to the efficient solution of non-local and fractional equations using iterative linear solvers. Non-local equations can be used to describe physical phenomena more accurately than classical local models. We introduce archetypes of elliptic and parabolic non-local equations, and state results concerning the regularity of their solution. We give details concerning finite element approximations and derive a priori and a posteriori error bounds. We then turn to the question of efficient implementation. We obtain sparse representations of the non-local operators by exploiting the low rank of off-diagonal blocks, and demonstrate that the assemble-solve-estimate-refine cycle has quasi-linear complexity. We give numerical examples, involving fractional Poisson and heat equations and reaction-diffusion systems. Advisors/Committee Members: Ainsworth, Mark (Advisor), Karniadakis, George (Reader), Guzman, Johnny (Reader).

▼ The Karhunen-Loeve (KL) decomposition provides a low dimensional representation for square integrable stochastic fields as it is optimal in the mean square sense. Despite the success of these methods for many stochastic systems of practical interest, potential roadblock occurs in strongly time-dependent problems. Motivated by this limitation, Sapsis and Lermusiaux(2009), developed the dynamically orthogonal(DO) framework, which allows for the simultaneous evolution of both the spatial basis and stochastic basis. Using the framework of Dynamical Orthogonality(DO) condition, a coupled set of evolution equations are derived for Allen-Cahn phase field transport equation. The reduced order field equations (DO equations) consists of (i) the system of Partial Differential equations(PDEs) that describes the evolution of the mean field and the orthonormal spatial basis(modes) defining the stochastic subspace where uncertainty "lives" and (ii) the set of Stochastic Differential equations(SDEs) that describes the evolution of stochastic basis(coefficients) defining how the stochasticity will be evolved within the reduced order stochastic subspace. Numerical simulations are performed for time independent high dimensional stochastic forcing based on Karhunen-Loeve(KL) decomposition. The aim of the current work is to investigate dimension reduction in high dimensional random space by analyzing the number of DO modes required to resolve the transient stochastic Allen-Cahn equation. Advisors/Committee Members: Karniadakis, George (Advisor).

▼ We discuss a discontinuous Galerkin (dG) method and its application to common partial differential equations which arise in the context of general relativity. First we consider extreme mass ratio binary (EMRB) systems. When modeling EMRBs as perturbations of a Schwarzschild black hole, the metric perturbations are described by the distributionally forced Regge-Wheeler-Zerilli (RWZ) equation. Despite the presence of jump discontinuities in the solution, our dG method achieves pointwise spectral accuracy. Particular attention is given to the common choice of trivialinitial data, and we show such unphysical specification may lead to spurious solutionswhich contaminate the physical solution indefinitely. Unintended consequences of thepersistent junk solution are considered as well as a simple prescription for removing it. Using our code we compute metric perturbations, gravitational waveforms, and self-force measurements from both circular and eccentric orbits.Next, we present a dG method for evolving the spherically reduced Generalized Baumgarte-Shapiro-Shibata-Nakamura (GBSSN) system expressed in terms of second-order spatial operators. Our multi-domain method achieves global spectralaccuracy and long-time stability on short computational domains. We discuss in detail both our scheme for the GBSSN system and its implementation. A theoretical and computational verification of the proposed scheme is given.We conclude with a preliminary look at reduced basis (RB) methods for parameterized binary systems. Our algorithm aims to construct a compact RB space from which a particular solution can be quickly and accurately recovered. We apply the algorithm to compress the space of analytic chirp gravitational waveforms. Next, the RWZ equation is revisited, and we consider extensions of the algorithm to a dG solver along with numerical evidence that a RB space exists for EMRB waveforms. Advisors/Committee Members: Hesthaven, Jan (Director), Guralnik, Gerald (Reader), Dell'Antonio, Ian (Reader).

▼ The positivity-preserving property is a highly desirable property when designing high order numerical methods for hyperbolic conservation laws, since negative values sometimes cause ill-posedness of the problem and blow-ups of the algorithms. The general framework for constructing positivity-preserving schemes for solving hyperbolic conservation laws have been proposed in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), pp.~3091 – 3120) and (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), pp.~8918 – 8934). In this dissertation, we extend this framework to DG methods with implicit discretizations and to DG methods for solving the relativistic hydrodynamics (RHD). Due to the the Courant-Friedrichs-Levis (CFL) number constraint, explicit DG methods are impractical for problems involving unstructured and extremely varying meshes or long-time simulations. Instead, implicit DG schemes are often popular in practice, especially in the computational fluid dynamics (CFD) community. In the first part of this dissertation, we develop a high-order positivity-preserving DG method with the backward Euler time discretization for solving conservation laws, basing on a generalization of the Zhang-Shu positivity-preserving limiter. Both the analysis and numerical experiments indicate that a lower bound for the CFL number is required to obtain the positivity-preserving property for the numerical schemes. The proposed method not only preserves the positivity of the numerical approximation without compromising the designed high-order accuracy, but also helps accelerate the convergence towards the steady-state solution and add robustness to the nonlinear solver. For RHD systems, the density and the pressure are positive physical quantities and the velocity is bounded by the speed of light. The violation of these bounds will result in ill-posedness of the problem and blow-up of the code, especially in extreme relativistic cases. It is usually hard to maintain these physical bounds without sacrificing the numerical accuracy. In the second part, we develop a bound-preserving DG method to solve RHD systems by extending the bound-preserving limiter for the non-relativistic hydrodynamics. The proposed method has the following features. It can theoretically guarantee to preserve the physical bounds for the numerical approximation and maintain its designed high order accuracy. Moreover, it renders L¹-stability to the numerical scheme. The robustness of the scheme is tested on various extreme relativistic cases, including relativistic jets. Advisors/Committee Members: Shu, Chi-Wang (Advisor), Guzman, Johnny (Reader), Darbon, Jerome (Reader).

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Heteroepitaxial thin films are essential components in many technological applications including optical, electronic and other functional devices. These films are also becoming important in the coating technologies for high-temperature materials applications. Typical heteroepitaxial systems involve one or more solid phases deposited on support structure called the substrate. Often the lattice and thermal mismatch in these systems results in significant elastic strains that, under the appropriate temperature conditions, drive mass transport by diffusion. Surface diffusion in these systems is usually a dominant mass transport mechanism that leads to morphological evolution of the surface. This evolution is called stress-driven morphological growth, and it has received much attention by materials modelers. In the current work, the problem of stress-driven morphological evolution in strained thin films is revisited; we develop a generalized formulation of this problem in the non-linear regime based upon a curvilinear coordinate formalism and finite element solution of the elastic sub-problem. This combination of methods facilitates the analysis of the onset of the instability and the early stage temporal evolution of the film surface. We apply our numerical scheme to surface wave, dot, pit, and ring morphologies and demonstrate the effects of model parameters on the incipient instabilities.

A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science.

Summer Semester, 2010.

June 28, 2010.

Thin Films, Instability, Epitaxy

Anter El-Azab, Professor Directing Thesis; Gordon Erlebacher, Committee Member.

Advisors/Committee Members: Anter El-Azab (professor directing thesis), Gordon Erlebacher (committee member).

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This thesis explores possible improvements in the construction of Delaunay Triangulations on the Sphere by designing and implementing a parallel alternative to the software package STRIPACK. First, it gives an introduction to Delaunay Triangulations on the plane and presents current methods available for their construction. Then, these concepts are mapped to the spherical case: Spherical Delaunay Triangulation (SDT). To provide a better understanding of the design choices, this document includes a brief overview of parallel programming, that is followed by the details of the implementation of the SDT generation code. In addition, it provides examples of resulting SDTs as well as benchmarks to analyze its performance. This project was inspired by the concepts presented in Robert Renka's work and was implemented in C++ using MPI.

A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science.

Spring Semester, 2011.

April 1, 2011.

Delaunay Triangulation, Spherical Delaunay Triangulation, Parallel Programming, Software Package

Max Gunzburger, Professor Directing Thesis; Anke Meyer-Baese, Committee Member; Janet Peterson, Committee Member; Jim Wilgenbusch, Committee Member.

Advisors/Committee Members: Max Gunzburger (professor directing thesis), Anke Meyer-Baese (committee member), Janet Peterson (committee member), Jim Wilgenbusch (committee member).

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In this thesis, we discuss the development of a new Boids system that simulates flocking behavior inside the Blender Game Engine and within the framework of the Real-Time Par- ticles System (RTPS) library developed by Ian Johnson. The collective behavior of Boids is characterized as an emergent behavior caused by following three steering behaviors: sep- aration, alignment, and cohesion. The implementation leverages OpenCL to maintain the portability of the Blender across different graphics cards and operating systems. Bench- marks of the RTPS-FLOCK system show that our implementation speeds up Blender's original Boids implementation (which only runs outside the game engine) by more than an order of magnitude. We demonstrate our boids system in three ways. First, we illustrate how symmetry of the steering behavior is maintained in time. Second, we consider the behavior of a "swarm of bees" approaching their hive. And third, we simulate the motion of a "crowd" constrained to a two-dimensional plane.

A Thesis Submitted to the Department of ScientifiC Computing in Partial FulfiLlment of the Requirements for the Degree of Master of Science.

Summer Semester, 2011.

June 24, 2011.

RTPS, Blender, boids, flocking

Gordon Erlebacher, Professor Directing Thesis; Ming Ye, Committee Member; Xiaoqiang Wang, Committee Member.

Advisors/Committee Members: Gordon Erlebacher (professor directing thesis), Ming Ye (committee member), Xiaoqiang Wang (committee member).

▼ Centroidal Voronoi tessellations (CVTs) are special Voronoi tessellations whose generators are also the centers of mass (centroids) of the Voronoi regions with respect to a given density function. CVT-based algorithms have been proved very useful in the context of image processing. However when dealing with the image segmentation problems, classic CVT algorithms are sensitive to noise. In order to overcome this limitation, we develop an edge-weighted centroidal Voronoi Tessellation (EWCVT) model by introducing a new energy term related to the boundary length which is called "edge energy". The incorporation of the edge energy is equivalent to add certain form of compactness constraint in the physical space. With this compactness constraint, we can effectively control the smoothness of the clusters' boundaries. We will provide some numerical examples to demonstrate the effectiveness, efficiency, flexibility and robustness of EWCVT. Because of its simplicity and flexibility, we can easily embed other mechanisms with EWCVT to tackle more sophisticated problems. Two models based on EWCVT are developed and discussed. The first one is "local variation and edge-weighted centroidal Voronoi Tessellation" (LVEWCVT) model by encoding the information of local variation of colors. For the classic CVTs or its generalizations (like EWCVT), pixels inside a cluster share the same centroid. Therefore the set of centroids can be viewed as a piecewise constant function over the computational domain. And the resulting segmentation have to be roughly the same with respect to the corresponding centroids. Inspired by this observation, we propose to calculate the centroids for each pixel separately and locally. This scheme greatly improves the algorithms' tolerance of within-cluster feature variations. By extensive numerical examples and quantitative evaluations, we demonstrate the excellent performance of LVEWCVT method compared with several state-of-art algorithms. LVEWCVT model is especially suitable for detection of inhomogeneous targets with distinct color distributions and textures. Based on EWCVT, we build another model for "Super-pixels" which is in fact a "regularization" of highly inhomogeneous images. We call our algorithm for super-pixels as "VCells" which is the abbreviation of "Voronoi cells". For a wide range of images, VCells is capable to generate roughly uniform sub-regions and meanwhile nicely preserves local image boundaries. The under-segmentation error is effectively limited in a controllable manner. Moreover, VCells is very efficient. The computational cost is roughly linear in image size with small constant coefficient. For megapixel sized images, VCells is able to generate very dense superpixels in a matter of seconds. We demonstrate that VCells outperforms several state-of-art algorithms through extensive qualitative and quantitative results on a wide range of complex images. Another important contribution of this work is the "Detecting-Segment-Breaking" (DSB) algorithm which can be used to guarantee the spatial… Advisors/Committee Members: Xiaoqiang Wang (professor directing dissertation), Xiaoming Wang (university representative), Max Gunzburger (committee member), Janet Peterson (committee member), Anter El-Azab (committee member).

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Parametric uncertainty analysis of surface complexation modeling (SCM) has been studied using linear and nonlinear analysis. A computational SCM model was developed by Kohler et al. (1996) to simulate the breakthrough of Uranium(VI) in a column of quartz. Calibration of parameters which describe the reactions involved during reactive-transport simulation has been found to fit experimental data well. Further uncertainty analysis has been conducted which determines the predictive capability of these models. It was concluded that nonlinear analysis results in a more accurate prediction interval coverage than linear analysis. An assumption made by both linear and nonlinear analysis is that the parameters follow a normal distribution. In a preliminary study, when using Monte Carlo sampling a uniform distribution among a known feasible parameter range, the model exhibits no predictive capability. Due to high parameter sensitivity, few realizations exhibit accuracy to the known data. This results in a high confidence of the calibrated parameters, but poor understanding of the parametric distributions. This study first calibrates these parameters using a global optimization technique, multi-start quasi-newton BFGS method. Second, a Morris method (MOAT) analysis is used to screen parametric sensitivity. It is seen from MOAT that all parameters exhibit nonlinear effects on the simulation. To achieve an approximation of the simulated behavior of SCM parameters without the assumption of a normal distribution, this study employs the use of a Covariance-Adaptive Monte Carlo Markov chain algorithm. It is seen from posterior distributions generated from accepted parameter sets that the parameters do not necessarily follow a normal distribution. Likelihood surfaces confirm the calibration of the models, but shows that responses to parameters are complex. This complex surface is due to a nonlinear model and high correlations between parameters. The posterior parameter distributions are then used to find prediction intervals about an experiment not used to calibrate the model. The predictive capability of Adaptive MCMC is found to be better than that of linear and non-linear analysis, showing a better understanding of parametric uncertainty than previous study.

A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science.

Spring Semester, 2011.

November 18, 2010.

Groundwater contamination, Hydrology

Ming Ye, Professor Directing Thesis; Robert van Engelen, Committee Member; Tomasz Plewa, Committee Member.

Advisors/Committee Members: Ming Ye (professor directing thesis), Robert Van Engelen (committee member), Tomasz Plewa (committee member).

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Long-chain branching affects the rheological properties of the polyethylenes strongly. Branching structure - density of branch points, branch length, and the locations of the branches - is complicated, therefore, without controlled branching structure it is almost impossible to study the effect of long-chain branching on the rheological properties. Single-site catalysts now make it possible to prepare samples in which the molecular weight distribution is relatively narrow and quite reproducible. In addition, a particular type of single-site catalyst, the constrained geometry catalyst, makes it possible to introduce low and well-controlled levels of long chain branching while keeping the molecular weight distribution narrow. Linear viscoelastic properties (LVE) of rheological properties contain a rich amount of data regarding molecular structure of the polymers. A computational algorithm that seeks to invert the linear viscoelastic spectrum of single-site metallocene-catalyzed polyethylenes is presented in this work. The algorithm uses a general linear rheological model of branched polymers as its underlying engine, and is based on a Bayesian formulation that transforms the inverse problem into a sampling problem. Given experimental rheological data on unknown single-site metallocene-catalyzed polyethylenes, it is able to quantitatively describe the range of values of weight-averaged molecular weight, MW, and average branching density, bm, consistent with the data. The algorithm uses a Markov-chain Monte Carlo method to simulate the sampling problem. If, and when information about the molecular weight is available through supplementary experiments, such as chromatography or light scattering, it can easily be incorporated into the algorithm, as demonstrated.

A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science.

Summer Semester, 2011.

June 3, 2011.

Bayesian, Polethylenes, Metallocene

Sachin Shanbhag, Professor Directing Thesis; Anter El-Azab, Committee Member; Peter Beerli, Committee Member.

Advisors/Committee Members: Sachin Shanbhag (professor directing thesis), Anter El-Azab (committee member), Peter Beerli (committee member).

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Spherical centroidal Voronoi tessellations (SCVT) are used in many applications in a variety of fields, one being climate modeling. They are a natural choice for spatial discretizations on the surface of the Earth. New modeling techniques have recently been developed that allow the simulation of ocean and atmosphere dynamics on arbitrarily unstructured meshes, including SCVTs. Creating ultra-high resolution SCVTs can be computationally expensive. A newly developed algorithm couples current algorithms for the generation of SCVTs with existing computational geometry techniques to provide the parallel computation of SCVTs and spherical Delaunay triangulations. Using this new algorithm, computing spherical Delaunay triangulations shows a speed up on the order of 4000 over other well known algorithms, when using 42 processors. As mentioned previously, newly developed numerical models allow the simulation of ocean and atmosphere systems on arbitrary Voronoi meshes providing a multi-resolution modeling framework. A multi-resolution grid allows modelers to provide areas of interest with higher resolution with the hopes of increasing accuracy. However, one method of providing higher resolution lowers the resolution in other areas of the mesh which could potentially increase error. To determine the effect of multi-resolution meshes on numerical simulations in the shallow-water context, a standard set of shallow-water test cases are explored using the Model for Prediction Across Scales (MPAS), a new modeling framework jointly developed by the Los Alamos National Laboratory and the National Center for Atmospheric Research. An alternative approach to multi-resolution modeling is Adaptive Mesh Refinement (AMR). AMR typically uses information about the simulation to determine optimal locations for degrees of freedom, however standard AMR techniques are not well suited for SCVT meshes. In an effort to solve this issue, a framework is developed to allow AMR simulations on SCVT meshes within MPAS. The resulting research contained in this dissertation ties together a newly developed parallel SCVT generator with a numerical method for use on arbitrary Voronoi meshes. Simulations are performed within the shallow-water context. New algorithms and frameworks are described and bench-marked.

A Dissertation submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Summer Semester, 2011.

June 14, 2011.

spherical centroidal voronoi tessellation, grid generation, high performance computing, spherical delaunay triangulation, adaptive mesh refinement, shallow-water equations, ocean modeling

Max Gunzburger, Professor Directing Thesis; Doron Nof, University Representative; Janet Peterson, Committee Member; Gordon Erlebacher, Committee Member; Michael Navon, Committee Member; John Burkardt, Committee Member; Todd Ringler, Committee Member.

Advisors/Committee Members: Max Gunzburger (professor directing thesis), Doron Nof (university representative), Janet Peterson (committee member), Gordon Erlebacher (committee member), Michael Navon (committee member), John Burkardt (committee member), Todd Ringler (committee member).

▼ We study the evolution of the collapsing core of a 15 solar mass blue supergiant supernova progenitor from the moment shortly after core bounce until 1.5 seconds later. We present a sample of two- and three-dimensional hydrodynamic models parameterized to match the explosion energetics of supernova SN 1987A. We focus on the characteristics of the flow inside the gain region and the interplay between hydrodynamics, self-gravity, and neutrino heating, taking into account uncertainty in the nuclear equation of state. We characterize the evolution and structure of the flow behind the shock in terms the accretion flow dynamics, shock perturbations, energy transport and neutrino heating effects, and convective and turbulent motions. We also analyze information provided by particle tracers embedded in the flow. Our models are computed with a high-resolution finite volume shock capturing hydrodynamic code. The code includes source terms due to neutrino-matter interactions from a light-bulb neutrino scheme that is used to prescribe the luminosities and energies of the neutrinos emerging from the core of the proto-neutron star. The proto-neutron star is excised from the computational domain, and its contraction is modeled by a time-dependent inner boundary condition. We find the spatial dimensionality of the models to be an important contributing factor in the explosion process. Compared to two-dimensional simulations, our three-dimensional models require lower neutrino luminosities to produce equally energetic explosions. We estimate that the convective engine in our models is 4% more efficient in three dimensions than in two dimensions. We propose that this is due to the difference of morphology of convection between two- and three-dimensional models. Specifically, the greater efficiency of the convective engine found in three-dimensional simulations might be due to the larger surface-to-volume ratio of convective plumes, which aids in distributing energy deposited by neutrinos. We do not find evidence of the standing accretion shock instability in our models. Instead we identify a relatively long phase of quasi-steady convection below the shock, driven by neutrino heating. During this phase, the analysis of the energy transport in the post-shock region reveals characteristics closely resembling that of penetrative convection. We find that the flow structure grows from small scales and organizes into large, convective plumes on the size of the gain region. We use tracer particles to study the flow properties, and find substantial differences in residency times of fluid elements in the gain region between two-dimensional and three-dimensional models. These appear to originate at the base of the gain region and are due to differences in the structure of convection. We also identify differences in the evolution of energy of the fluid elements, how they are heated by neutrinos, and how they become gravitationally unbound. In particular, at the time when the explosion commences, we find that the unbound material has relatively… Advisors/Committee Members: Tomasz Plewa (professor directing dissertation), Mark Sussman (university representative), Anke Meyer-Baese (committee member), Gordon Erlebacher (committee member), Ionel M. Navon (committee member).

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This dissertation studies a graphical processing unit (GPU) construction of Bayesian neural networks (BNNs) using large training data sets. The goal is to create a program for the mapping of phenomenological Minimal Supersymmetric Standard Model (pMSSM) parameters to their predictions. This would allow for a more robust method of studying the Minimal Supersymmetric Standard Model, which is of much interest at the Large Hadron Collider (LHC) experiment CERN. A systematic study of the speedup achieved in the GPU application compared to a Central Processing Unit (CPU) implementation are presented.

A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Spring Semester, 2014.

April 1, 2014.

Bayesian Neural Networks, GPU, pMSSM, Scientific Computing

Anke Meyer-Baese, Professor Directing Dissertation; Harrison Prosper, Professor Directing Dissertation; Jorge Piekarewicz, University Representative; Sachin Shanbhag, Committee Member; Peter Beerli, Committee Member.

Advisors/Committee Members: Anke Meyer-Baese (professor directing dissertation), Harrison Prosper (professor directing dissertation), Jorge Piekarewicz (university representative), Sachin Shanbhag (committee member), Peter Beerli (committee member).

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The tools and techniques used in shape analysis have constantly evolved, but their objective remains fixed: to quantify the differences in shape between two objects in a consistent and meaningful manner. The hand-measurements of calipers and protractors of the past have yielded to laser scanners and landmark-placement software, but the process still involves transforming an object's physical shape into a concise set of numerical data that can be readily analyzed by mathematical means [Rohlf 1993]. In this paper, we present a new method to perform this transformation by taking full advantage of today's high-power computers and high-resolution scanning technology. This method uses surface scans to calculate a shape-difference metric and perform superimposition rather than relying on carefully (and tediously) placed manual landmarks. This is accomplished by building upon and extending the Iterative Closest Point algorithm. We also examine some new ways this data may be used; we can, for example, calculate an averaged surface directly and visualize point-wise shape information over this surface. Finally, we demonstrate the use of this method on a set of primate skulls and compare the results of the new methodology with traditional geometric morphometric analysis.

A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science.

Fall Semester, 2013.

October 11, 2013.

GPSA, Heat Maps, ICP, Morphometrics, Procrustes

Dennis Slice, Professor Directing Thesis; Peter Beerli, Committee Member; Sachin Shanbhag, Committee Member.

Advisors/Committee Members: Dennis Slice (professor directing thesis), Peter Beerli (committee member), Sachin Shanbhag (committee member).

▼ A theoretical-computational model is developed to study irradiation-induced composition patterns and segregation in binary solid solutions under irradiation, which is motivated by the fact that such composition changes alter a wide range of metallurgical properties of structural alloys used in the nuclear industry. For a binary alloy system, the model is based on a coupled, nonlinear set of reaction-diffusion equations for six defect and atomic species, which include vacancies, three interstitial dumbbell configurations, and the two alloy elements. Two sets of boundary conditions have been considered: periodic boundary conditions, which are used to investigate composition patterning in bulk alloys under irradiation, and reaction boundary conditions to study the radiation-induced segregation at surfaces. Reactions are considered to be either between defects, which is called recombination, or between defects and alloying elements, which result in change in the interstitial dumbbell type. Long range diffusion of all the species is considered to happen by vacancy and interstitialcy mechanisms. As such, diffusion of the alloy elements is coupled to the diffusion of vacancies and interstitials. Defect generation is considered to be associated with collision cascade events that occur randomly in space and time. Each event brings about a change in the local concentration of all the species over the mesoscale material volume affected by the cascade. Stiffly-stable Gear's method has been implemented to solve the reaction-diffusion model numerically. Gear's method is a variant of higher order implicit linear multi-step method, implemented in predictor-corrector fashion. The resulting model has been tested with a miscible CuAu solid solution. For this alloy, and in the absence of boundaries, steady state composition patterns of several nanometers have been observed. Fourier space properties of these patterns have been found to depend on irradiation-specific control parameters, temperature, and initial state of the alloy. Linear stability analysis of the set of reaction-diffusion equations confirms the findings of the numerical simulations. In the presence of boundaries, radiation-induced segregation of alloying species has been observed near in the boundary layer: enrichment of faster diffusing species and depletion of slower diffusing species. Radiation-induced segregation has also been found to depend upon irradiation-specific control parameters and temperature. The results show that the degree of segregation is spatially non-uniform and hence it should be studied in higher dimensions. Proper formulation of the boundary conditions showed that segregation of the alloy elements to the boundary is coupled to the boundary motion. With both patterning and segregation investigations, the irradiated sample has been found to recover its uniform state with time when irradiation is turned off. The inference drawn out from this observation is that in miscible solid solutions irradiation-induced composition patterning and… Advisors/Committee Members: Anter El Azab (professor directing thesis), Per Arne Rikvold (university representative), Sachin Shanbhag (committee member), Gordon Erlebacher (committee member), Tomasz Plewa (committee member).

▼ Estimating groundwater nitrate fate and transport is an important task in water resources and environmental management because excess nitrate loads may have negative impacts on human and environmental health. This work discusses the development of a simplified nitrate transport model and its implementation as a geographic information system (GIS)-based screening tool, whose purpose is to estimate nitrate loads to surface water bodies from onsite wastewater-treatment systems (OWTS). Key features of this project are the reduced data demands due to the use of a simplified model, as well as ease of use compared to traditional groundwater flow and transport models, achieved by embedding the model within a GIS. The simplified conceptual model consists of a simplified groundwater flow model in the surficial aquifer, and a simplified transport model that makes use of an analytical solution to the advection-dispersion equation, used for determining nitrate fate and transport. Denitrification is modeled using first order decay in the analytical solution with the decay constant obtained from literature and/or site-specific data. The groundwater flow model uses readily available topographic data to approximate the hydraulic gradient, which is then used to calculate seepage velocity magnitude and direction. The flow model is evaluated by comparing the results to a previous numerical modeling study of the U.S. Naval Air Station, Jacksonville (NAS) performed by the USGS. The results show that for areas in the vicinity of the NAS, the model is capable of predicting groundwater travel times from a source to a surface water body to within ±20 years of the USGS model, 75% of the time. The transport model uses an analytical solution based on the one by Domenico and Robbins (1985), the results of which are then further processed so that they may be applied to more general, real-world scenarios. The solution, as well as the processing steps are tested using artificially constructed scenarios, each meant to evaluate a certain aspect of the solution. For comparison purposes, each scenario is solved using a well known numerical contaminant transport model. The results show that the analytical solution provides a reasonable approximation to the numerical result. However, it generally underestimates the concentration distribution to varying degrees depending on choice of parameters, especially along the plume centerline. These results are in agreement with previous studies (Srinivasan et al., 2007; West et al., 2007). The adaptation of the analytical solution to more realistic scenarios results in an adequate approximation to the numerically calculated plume, except in areas near the advection front, where the model produces a plume whose shape differs noticeably from the numerical solution. Load calculations are carried out using a mass balance approach where the system is considered to be in the steady state. The steady-state condition allows for a load estimate by subtracting the mass removal rate due to denitrification from the input mass… Advisors/Committee Members: Ming Ye (professor directing thesis), Janet Peterson (committee member), Sachin Shanbhag (committee member), James Wilgenbusch (committee member).

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Hydrodynamic instabilities are the driving force behind complex fluid processes that occur from everyday scenarios to the most extreme physical conditions of the universe. The Rayleigh-Taylor instability (RTI) develops when a heavy fluid is accelerated by a light fluid, resulting in sinking spikes, rising bubbles, and material mixing. Laser experiments have observed features of RTI that cannot be explained with pure hydrodynamic models. For this computational study we have implemented and verified extended physics mod- ules for anisotropic thermal conduction and self-generated magnetic fields in the FLASH- based Proteus code using the Braginskii plasma theory. We have used this code to simulate RTI in a basic plasma physics context. We obtain results up to 35 nanoseconds (ns) at various resolutions and discuss convergence and computational challenges. We find that magnetic fields as high as 1-10 megagauss (MG) are genereated near the fluid interface. Thermal conduction turns out to be essentially isotropic in these conditions, but plays the dominant role in the evolution of the system by smearing out small-scale structure and reducing the RT growth rate. This may account for the relatively feature- less RT spikes seen in experiments. We do not, however, observe mass extensions in our simulations. Without thermal conductivity, the magnetic field has the effect of generating what appears to be an additional RT mode which results in new structure at later times, when compared to pure hydro models. Additional physics modules and 3-D simulations are needed to complete our Braginskii model of RTI.

A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science.

Summer Semester, 2012.

June 29, 2012.

astrophysics, computational, magnetic, physics, plasma, thermal

Tomasz Plewa, Professor Directing Thesis; Michael Ionel Navon, Committee Member; Mark Sussman, Committee Member.

Advisors/Committee Members: Tomasz Plewa (professor directing thesis), Michael Ionel Navon (committee member), Mark Sussman (committee member).

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In the present work, we investigate the internal fields generated by the dislocation structures that form during the deformation of copper single crystals. In particular, we perform computational modeling of the statistical and morphological characteristics of the dislocation structures obtained by dislocation dynamics simulation method and compare the results with X-ray microscopy measurements of the same data. This comparison is performed for both the dislocation structure and their internal elastic fields for the cases of homogeneous deformation and indentation of copper single crystals. A direct comparison between dislocation dynamics predictions and X-ray measurements plays a key role in demonstrating the fidelity of discrete dislocation dynamics as a predictive computational mechanics tool and in understanding the X-ray data. For the homogeneous deformation case, dislocation dynamics simulations were performed under periodic boundary conditions and the internal fields of dislocations were computed by solving an elastic boundary value problem of many-dislocation system using the finite element method. The distribution and pair correlation functions of all internal elastic fields and the dislocation density were computed. For the internal stress field, the availability of such statistical information paves the way to the development of a density-based mobility law of dislocations in continuum dislocation dynamics models, by correlating the internal-stress statistics with dislocation velocity statistics. The statistical analysis of the lattice rotation and the dislocation density fields in the deformed crystal made possible the direct comparison with X-ray measurements of the same data. Indeed, a comparison between the simulation and experimental measurements has been possible, which revealed important aspects of similarity and differences between the simulation results and the experimental data. In the case of indentation, which represents a highly inhomogeneous deformation, a contact boundary value problem was solved in conjunction with a discrete-dislocation dynamics simulation model; the discrete dislocation dynamics simulation was thus enabled to handle finite domains under mixed traction/displacement boundary conditions. The load-displacement curves for indentation experiments were analyzed with regard to cross slip, indentation speed and indenter shape. The lattice distortion fields obtained by indentation simulations were directly compared with their experimental counterparts. Other indentation simulations were also carried out, giving insight into different aspects of micro-scale indentation deformation.

A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Fall Semester, 2012.

November 2, 2012.

Copper, Dislocation Dynamics, Indentation, Plasticity, Size effects

Anter El-Azab, Professor Directing Thesis; Leon van Dommelen, University Representative; Gordon Erlebacher, Committee Member; Ming Ye,…

Advisors/Committee Members: Anter El-Azab (professor directing thesis), Leon Van Dommelen (university representative), Gordon Erlebacher (committee member), Ming Ye (committee member), Xiaoqiang Wang (committee member).

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A significant component of forensic science is analyzing bones to assess the age at death of an individual. Forensic anthropologists often include the pubic symphysis in such studies. Subjective methods, such as the Suchey-Brooks method, are currently used to analyze the pubic symphysis. This thesis examines a more objective, quantitative method. The method analyzes 3D surface scans of the pubic symphysis and implements a thin plate spline algorithm which models the bending of a flat plane to approximately match the surface of the bone. The algorithm minimizes the bending energy required for this transformation. Results presented here show that there is a correlation between the minimum bending energy and the age at death of the individual. The method could be useful to medico-legal practitioners.

A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science.

Fall Semester, 2012.

August 8, 2012.

Age estimation, Pubis Symphysis, Thin plate splines

Dennis Slice, Professor Directing Thesis; John Burkardt, Committee Member; Ming Ye, Committee Member; Sachin Shanbhag, Committee Member.

Advisors/Committee Members: Dennis Slice (professor directing thesis), John Burkardt (committee member), Ming Ye (committee member), Sachin Shanbhag (committee member).

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Heat is transfered in crystalline semiconductor materials via lattice vibrations. Lattice vibrations are treated with a wave-particle duality just like photons are quantum mechanical representations of electro-magnetic waves. The quanta of energy of these lattice waves are called phonons. The Boltzmann Transport Equation (BTE) has proved to be a powerful tool in modeling the phonon heat conduction in crystalline solids. The BTE tracks the phonon number density function as it evolves according to the drift of all phonons and to the phonon-phonon interactions (or collisions). Unlike Fourier's law which is limited to describing diffusive energy transport, the BTE can accurately predict energy transport in both ballistic (virtually no collisions) and diffuse regimes. Motivated by the need to understand thermal transport in irradiated Uranium Dioxide at the mesoscale, this work investigates phonon transport in UO2 using Monte Carlo simulation. The simulation scheme aims to solve the Boltzmann transport equation for phonons within a relaxation time approximation. In this approximation the Boltzmann transport equation is simplified by assigning time scales to each scattering mechanism associated with phonon interactions. The Monte Carlo method is first benchmarked by comparing to similar models for silicon. Unlike most previous works on solving this equation by Monte Carlo method, the momentum and energy conservation laws for phonon-phonon interactions in UO2 are treated exactly; in doing so, the magnitude of possible wave vectors and frequency space are all discretized and a numerical routine is then implemented which considers all possible phonon-phonon interactions and chooses those interactions which obey the conservation laws. The simulation scheme accounts for the acoustic and optical branches of the dispersion relationships of UO2. The six lowest energy branches in the [001] direction are tracked within the Monte Carlo. Because of their predicted low group velocities, the three remaining, high-energy branches are simply treated as a reservoir of phonons at constant energy in K-space. These phonons contribute to the thermal conductivity only by scattering with the six lower energy branches and not by their group velocities. Using periodic boundary conditions, this work presents results illustrating the diffusion limit of phonon transport in UO2 single crystals, and computes the thermal conductivity of the material in the diffusion limit based on the detailed phonon dynamics. The temperature effect on conductivity is predicted and the results are compared with experimental data available in the literature.

A Thesis submitted to the Department of ScientifiC Conmputing in partial fulfillment of the requirements for the degree of Master of Science.

Fall Semester, 2011.

November 7, 2011.

Boltzmann, Carlo, Monte, Phonon, Thermal, Transport

Anter El-Azab, Professor Directing Thesis; Tomasz Plewa, Committee Member; Xiaoqiang Wang, Committee Member.

Advisors/Committee Members: Anter El-Azab (professor directing thesis), Tomasz Plewa (committee member), Xiaoqiang Wang (committee member).

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In response to potential increasing rate of sea-level rise, planners and engineers are making accommodations in their management plans for protection of coastal infrastructure and natural resources. Dunes and barrier islands are important for coastal protection and restoration, because they absorb storm energy and play an essential role in sediment transportation. Most of traditional coastal models do not simulate joint evolution of dunes and barrier islands and do not explicitly address sea-level rise. A new model was developed in this study that represents basic barrier island processes under sea-level rise and links dynamics of different components of barrier islands. The model was used to evaluate near-future (100 years) responses of a semi-synthetic island, with the characteristics of Santa Rosa Island of Florida, USA, to five rates of sea-level rise. The new model is capable of representing considerable practical information about effects of different sea level rise scenarios on the test island. The modeling results show that different areas and components of the island have different responses to sea-level rise. Depending on the rate of sea level rise and overwash sediment supply, evolution of dunes and barrier islands is important to habitat suitable for coastal birds or to backbarrier salt marshes. The modeling results are inherently uncertain due to unknown storm variability and sea-level rise scenarios. The storm uncertainty, characterized as parametric uncertainty, and its propagation to the modeling results, were assessed using the Monte Carlo (MC) method for the synthetic barrier island. A total of 1000 realizations of storm magnitude, frequency, and track through a barrier island were generated and used for the MC simulation. To address the scenario uncertainty, five sea-level rise scenarios were considered using the current rate and four additional rates that lead to sea-level rise of to 0.5m, 1.0m, 1.5m, and 2.0m in the next 100 years. Parametric uncertainty in the simulated beach dune heights and the backshore positions was assessed for the individual scenarios. For a given scenario, the parametric uncertainty varies with time, becoming larger when time increases. For different sea-level rise scenarios, the parametric uncertainty is different, being larger for more severe sea-level rise. The method of scenario averaging was used to quantify the scenario uncertainty. The scenario averaging results are between the results of smallest and largest sea-level rise scenarios. The results of uncertainty analysis provide guidelines for coastal management and protection of coastal ecology.

A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science.

Fall Semester, 2011.

November 3, 2011.

barrier island, morphology, sea-level rise, storm

Ming Ye, Professor Directing Thesis; Dennis Slice, Committee Member; Tomasz Plewa, Committee Member.

Advisors/Committee Members: Ming Ye (professor directing thesis), Dennis Slice (committee member), Tomasz Plewa (committee member).

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The primary hydrodynamic flow feature of early explosion phases of a core-collapse supernova is a spherical shock. This shock is born deep in the central regions of the collapsing stellar core, stalls shortly afterward, and in case of a successful explosion is revived and becomes the supernova shock. The revival process involves a standing accretion shock instability, SASI. This shock instability is considered the key processes aiding the core-collapse supernova (ccSN) explosion. The aim of our study is to identify feasible conditions and parameters for an experimental system that is able to capture the essential characteristics of SASI. We use analytic methods and high-resolution hydrodynamic simulations in multidimensions to investigate a possible experimental design on the National Ignition Facility. The experimental configuration involves a steady, spherical shock. We explore a viable region of parameters and obtain limits on the shocked flow geometry. We study the stability properties of the shock and its post-shock region. We discuss key differences between the experimental setup and astrophysical environment. The obtained flowfield closely resembles conveging nozzle flow. The post-shock region, in contrast to the supernova setting, is found to be stably stratified and insensitive to perturbations upstream of the shock. We conclude that it is not possible to capture the characteristics of the supernova SASI for the converging shocked flow configuration considered here. However, such configuration offers a very stable setting for precision studies of shocked, dense, high temperature plasmas requiring finely-controlled conditions.

A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science.

Fall Semester, 2011.

October 21, 2011.

hydrodynamics, laboratory astrophysics, shockwaves, supernovae

Tomasz Plewa, Professor Directing Thesis; Gordon Erlebacher, Committee Member; Michael Navon, Committee Member.

Advisors/Committee Members: Tomasz Plewa (professor directing thesis), Gordon Erlebacher (committee member), Michael Navon (committee member).

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In this dissertation, the recently developed peridynamic nonlocal continuum model for solid mechanics is extensively studied, specifically, the numerical methods for the deterministic and stochastic steady-state peridynamics models. In contrast to the classical partial differential equation models, peridynamic model is an integro-differential equation that does not involve spatial derivatives of the displacement field. As a result, the peridynamic model admits solutions having jump discontinuities so that it has been successfully applied to the fracture problems. This dissentation consists of three major parts. The first part focuses on the one-dimensional steady-state peridynamics model. Based on a variational formulation, continuous and discontinuous Galerkin finite element methods are developed for the peridynamic model. Optimal convergence rates for different continuous and discontinuous manufactured solutions are obtained. A strategy for identifying the discontinuities of the solution is developed and implemented. The convergence of peridynamics model to classical elasticity model is studied. Some relevant nonlocal problems are also considered. In the second part, we focus on the two-dimensional steady-state peridynamics model. Based on the numerical strategies and results from the one-dimensional peridynamics model, we developed and implemented the corresponding approaches for the two-dimensional case. Optimal convergence rates for different continuous and discontinuous manufactured solutions are obtained. In the third part, we study the stochastic peridynamics model. We focus on a version of peridynamics model whose forcing terms are described by a finite-dimensional random vector, which is often called the finite-dimensional noise assumption. Monte Carlo methods, stochastic collocation with full tensor product and sparse grid methods based on this stochastic peridynamics model are implemented and compared.

A Dissertation submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Summer Semester, 2012.

June 22, 2012.

DISCONTINUOUS GALEKIN METHODS, FINITE ELEMENT METHODS, INTEGRAL DIFFERENTIAL EQUATIONS, NONLOCAL DIFFUSION PROBLEM, PERIDYNAMICS, STOCHASTIC

Max Gunzburger, Professor Directing Dissertation; Xiaoming Wang, University Representative; Janet Peterson, Committee Member; Xiaoqiang Wang, Committee Member; Ming Ye, Committee Member; John Burkardt, Committee Member.

Advisors/Committee Members: Max Gunzburger (professor directing dissertation), Xiaoming Wang (university representative), Janet Peterson (committee member), Xiaoqiang Wang (committee member), Ming Ye (committee member), John Burkardt (committee member).

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Prediction markets are forums of trade where contracts on the future outcomes of events are bought and sold. These contracts reward buyers based on correct predictions and thus give incentive to make accurate predictions. Prediction markets have successfully predicted the outcomes of sporting events, elections, scientific hypothesese, foreign affairs, etc... and have repeatedly demonstrated themselves to be more accurate than individual experts or polling [2]. Since prediction markets are aggregation mechanisms, they have garnered interest in the machine learning community. Artificial prediction markets have been successfully used to solve classification problems [34, 33]. This dissertation explores the underlying optimization problem in the classification market, as presented in [34, 33], proves that it is related to maximum log likelihood, relates the classification market to existing machine learning methods and further extends the idea to regression and density estimation. In addition, the results of empirical experiments are presented on a variety of UCI [25], LIAAD [49] and synthetic data to demonstrate the probability accuracy, prediction accuracy as compared to Random Forest [9] and Implicit Online Learning [32], and the loss function.

A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Spring Semester, 2013.

March 29, 2013.

Aggregation, Artificial Prediction Markets, Classification, Density estimation, Machine Learning, Regression

Adrian Barbu, Professor Directing Thesis; Anke Meyer-Baese, Professor Co-Directing Thesis; Debajyoti Sinha, University Representative; Ye Ming, Committee Member; Xiaoqiang Wang, Committee Member.

Advisors/Committee Members: Adrian Barbu (professor directing thesis), Anke Meyer-Baese (professor co-directing thesis), Debajyoti Sinha (university representative), Ye Ming (committee member), Xiaoqiang Wang (committee member).

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This dissertation presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT) which are to be used for multiphysics, multidomain applications. As an introduction, we discuss grid generation on the sphere in a broad fashion. Next, we discuss the theory of CVTs in general, and specifically on the sphere. Subsequently we consider the iterative processes, such as Lloyd's algorithm, which are used to construct them. Following this, we describe a method for density functions via images so that we can shape generator density in an intuitive, yet arbitrary, manner, and then a method by which SCVTs can be easily adapted to conform to arbitrary sets of line segments, or shorelines. Then, we discuss sample meshes, used for various physical and nonphysical applications. Penultimately, we discuss two sample applications, as a proof of concept, where we adapt the Shallow Water Model from Model for Predictions Across Scales (MPAS) to use our grids for a more accurate border, and we also discuss elliptic interface problems both with and without hanging nodes. Finally, we share a few concluding remarks.

A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Fall Semester, 2011.

November 3, 2011.

Max Gunzburger, Professor Co-Directing Dissertation; Janet Peterson, Professor Co-Directing Dissertation; Kyle Gallivan, University Representative; Gordon Erlebacher, Committee Member; Xiaoqiang Wang, Committee Member; Todd Ringler, Committee Member.

Advisors/Committee Members: Max Gunzburger (professor co-directing dissertation), Janet Peterson (professor co-directing dissertation), Kyle Gallivan (university representative), Gordon Erlebacher (committee member), Xiaoqiang Wang (committee member), Todd Ringler (committee member).

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Advances in computational power have lead to many developments in science and en- tertainment. Powerful simulations which required expensive supercomputers can now be carried out on a consumer personal computer and many children and young adults spend countless hours playing sophisticated computer games. The focus of this research is the development of tools which can help bring the entertaining and appealing traits of video games to scientific education. Video game developers use many tools and programming languages to build their games, for example the Blender 3D content creation suite. Blender includes a Game Engine that can be used to design and develop sophisticated interactive experiences. One important tool in computer graphics and animation is the particle system, which makes simulated effects such as fire, smoke and fluids possible. The particle system available in Blender is unfortunately not available in the Blender Game Engine because it is not fast enough to run in real-time. One of the main factors contributing to the rise in computational power and the increas- ing sophistication of video games is the Graphics Processing Unit (GPU). Many consumer personal computers are equipped with powerful GPUs which can be harnassed for general purpose computation. This thesis presents a particle system library is accelerated by the GPU using the OpenCL programming language. The library integrated into the Blender Game Engine providing an interactive platform for exploring fluid dynamics and creating video games with realistic water effects. The primary system implemented in this research is a fluid sim- ulator using the Smoothed Particle Hydrodynamics technique for simulating incompressible fluids such as water. The library created for this thesis can simulate water using SPH at 40fps with upwards x  of 100,000 particles on an NVIDIA GTX480 GPU. The fluid system has interactive features such as object collision, and the ability to add and remove particles dynamically. These features as well as phsyical properties of the simulation can be controlled intuitively from the user interface of Blender.

A Thesis submitted to the Department of ScientifiC Computing in partial fulfillment of the requirements for the degree of Master of Science.

Fall Semester, 2011.

August 24, 2011.

Game Design, GPU, OpenCL, SPH

Gordon Erlebacher, Professor Directing Thesis; Tomasz Plewa, Committee Member; Anter El-Azab, Committee Member.

Advisors/Committee Members: Gordon Erlebacher (professor directing thesis), Tomasz Plewa (committee member), Anter El-Azab (committee member).

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This dissertation compares and contrasts large-scale optimization algorithms in the use of variational and sequential data assimilation on two novel problems chosen to highlight the challenges in non-linear and non-smooth data assimilation. The first problem explores the impact of a highly non-linear observation operator and highlights the importance of background information on the data assimilation problem. The second problem tackles large-scale data assimilation with a non-smooth observation operator. Together, these two cases show both the importance of choosing an appropriate data assimilation method and, when a variational or variationally-inspired method is chosen, the importance of choosing the right optimization algorithm for the problem at hand.

A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Spring Semester, 2012.

November 21, 2011.

All-sky infrared satellite, Cloudy IR, Inverse problem, Limited Memory Bundle Method, Non-differentiable, Quasi-Newton

Ionel Michael Navon, Professor Directing Thesis; Guosheng Liu, University Representative; Max Gunzburger, Committee Member; Gordon Erlebacher, Committee Member; Milijia Zupanski, Committee Member; Napsu Karmitsa, Committee Member.

Advisors/Committee Members: Ionel Michael Navon (professor directing thesis), Guosheng Liu (university representative), Max Gunzburger (committee member), Gordon Erlebacher (committee member), Milijia Zupanski (committee member), Napsu Karmitsa (committee member).

▼ The Internet email system as a popular online communication tool has been increasingly misused by ill-willed users to carry out malicious activities including spamming and phishing. Alarmingly, in recent years the nature of the email-based malicious activities has evolved from being purely annoying (with the notorious example of spamming) to being criminal (with the notorious example of phishing). Despite more than a decade of anti-spam and anti-phishing research and development efforts, both the sophistication and volume of spam and phishing messages on the Internet have continuously been on the rise over the years. A key difficulty in the control of email-based malicious activities is that malicious actors have great operational flexibility in performing email-based malicious activities, in terms of both the email delivery infrastructure and email content; moreover, existing anti-spam and anti-phishing measures allow for arms race between malicious actors and the anti-spam and anti-phishing community. In order to effectively control email-based malicious activities such as spamming and phishing, we argue that we must limit (and ideally, eliminate) the operational flexibility that malicious actors have enjoyed over the years. In this dissertation we develop and evaluate a sender-centric approach (SCA) to addressing the problem of email-based malicious activities so as to control spam and phishing emails on the Internet. SCA consists of three complementary components, which together greatly limit the operational flexibility of malicious actors in sending spam and phishing emails. The first two components of SCA focus on limiting the infrastructural flexibility of malicious actors in delivering emails, and the last component focuses on on limiting the flexibility of malicious actors in manipulating the content of emails. In the first component of SCA, we develop a machine-learning based system to prevent malicious actors from utilizing compromised machines to send spam and phishing emails. Given that the vast majority of spam and phishing emails are delivered via compromised machines on the Internet today, this system can greatly limit the infrastructural flexibility of malicious actors. Ideally, malicious actors should be forced to send spam and phishing messages from their own machines so that blacklists and reputation-based systems can be effectively used to block spam and phishing emails. The machine-learning based system we develop in this dissertation is a critical step towards this goal. In recent years, malicious actors also started to employ advanced techniques to hijack network prefixes in conducting email-based malicious activities, which makes the control and attribution of spam and phishing emails even harder. In the second component of SCA, we develop a practical approach to improve the security of the Internet inter-domain routing protocol BGP. Given that the key difficulties in adopting any mechanism to secure the Internet inter-domain routing are the overhead and incremental deployment property of the… Advisors/Committee Members: Zhenhai Duan (committee member), Xufeng Niu (university representative), Xin Yuan (committee member), Sudhir Aggarwal (committee member).