Numerical Analysis and Scientific Computing Commons^™

Information Theory Analysis Of Water Vapor Stable Isotopes From The Sail Campaign, Matthew John Rybecky

Earth and Planetary Sciences ETDs

Understanding the processes that control water vapor isotopic composition in mountain environ- ments is essential for interpreting isotope records and predicting water resource responses to cli- mate change. This thesis applies information theory to continuous, high-resolution water vapor stable isotope measurements from the Surface Atmosphere Integrated Field Laboratory (SAIL) campaign in the East River watershed of Colorado’s Upper Gunnison Basin, spanning the winter- to-spring transition of 2022–2023. The analysis employs Shannon entropy, mutual information, transfer entropy, and joint transfer en- tropy (JTE) to quantify how environmental variables, including surface meteorology, radiation, tur- bulent fluxes, and ERA5 reanalysis products, transfer information …

Algebraic Multigrid Methods For Nonsymmetric And Indefinite Problems: Theory And Applications, Ahsan Ali

Mathematics & Statistics ETDs

Algebraic multigrid (AMG) is a well-established and highly efficient solver for symmetric positive definite (SPD) systems arising from elliptic and parabolic PDEs, while nonsymmetric systems from hyperbolic PDEs remain a significant challenge. This dissertation develops AMG methods and theory for nonsymmetric problems. First, we develop a novel approach combining mode constraints from energy-minimization AMG with local approximations of ideal restriction in $\ell$AIR, resulting in constrained $\ell$AIR (C$\ell$AIR), which demonstrates scalable convergence across advective and diffusive problems. Second, we extend optimal AMG theory by deriving spectral radius estimates for the two-grid error transfer operator using matrix-induced orthogonality, enabling convergence predictions for …

Optimizing Distributed Boundary Exchanges For Benchmarks, Solvers And Sparse Matrix Operations, Gerald Collom

Computer Science ETDs

Boundary exchanges dominate the cost of both stenciled codes and those that rely on sparse matrix operations. The performance of large boundary exchanges is limited by synchronization overheads and injection bandwidth limitations. Irregular boundary exchanges incur additional overheads due to the large number of required messages. This thesis investigates multiple methods for improving the performance and scalability of both Cartesian and irregular boundary exchanges. Since boundary exchanges are typically performed iteratively, persistent communication presents an opportunity for optimization by sharing and amortizing setup costs. Partitioned communication is also explored to increase asynchrony, reducing bottlenecks from synchronization overheads and data congestion. …

Parallel Multigrid In Time For Chaotic Dynamical Systems, David Alan Vargas

Mathematics & Statistics ETDs

Despite the fact that Parallel-in-Time (PinT) methods are predicted to become necessary to fully utilize next-generation exa- and zettascale machines, there are currently no known practical methods which scale well with the length of the time-domain for chaotic problems, due to exponential dependence of the condition number on the fastest chaotic timescale. I present modifications to the coarse-grid equations along with a novel rediscretization approach which together greatly improve convergence of the multigrid reduction in time (MGRIT) algorithm and allow the first known PinT speedup for a chaotic PDE. The novel Local Shadowing Relaxation (LSR) is presented as an alternative …

Analysis And Computation Of Constrained Sparse Coding On Emerging Non-Von Neumann Devices, Kyle Henke

Mathematics & Statistics ETDs

This dissertation seeks to understand how different formulations of the neurally inspired Locally Competitive Algorithm (LCA) represent and solve optimization problems. By studying these networks mathematically through the lens of dynamical and gradient systems, the goal is to discern how neural computations converge and link this knowledge to theoretical neuroscience and artificial intelligence (AI). Both classical computers and advanced emerging hardware are employed in this study. The contributions of this work include:

1. Theoretical Work: A comprehensive convergence analysis for networks using both generic Rectified Linear Unit (ReLU) and Rectified Sigmoid activation functions. Exploration of techniques to address the binary …

Mathematically Rigorous Deep Learning Paradigms For Data-Driven Scientific Modeling, Owen Nicholas Davis

Mathematics & Statistics ETDs

This dissertation explores the crucial role of data-driven modeling in science and engineering, with a focus on developing surrogate models to accelerate large-scale computational tasks, aiding in both outer-loop functions like uncertainty quantification and expensive inner-loop tasks within broader computational frameworks. Challenges arise with increased problem dimension and sparse, noisy training data, particularly significant when constructing surrogates for very expensive computational models where acquiring sufficient high-fidelity training data is unfeasible. In such scenarios, training surrogates from an ensemble of multifidelity information sources of varying accuracy and cost becomes essential. We emphasize neural network-based modeling paradigms, which are flexible in integrating …

Fiesta And Shock-Driven Flows, Brian E. Romero

Mechanical Engineering ETDs

In this study, the interaction of a shock with various gas and particle interfaces is analyzed through simulations using a new, GPU capable, multi-species flow solver, FIESTA (Fast, Interface Evolution, Shocks, and Transport in the Atmosphere), de- veloped for this research. The cases studied include the interaction between a shock and i) a two-dimensional (2D), circular cloud of a dense gas; ii) a 2D curtain of a dense gas; iii) a three-dimensional (3D) cylinder of a dense gas, and iv) a 3D curtain of solid particles.

In simulations of a 2D gas curtain and a 3D gas column, the curtain …

Statistical Modeling Of Hpc Performance Variability And Communication, Jered B. Dominguez-Trujillo

Computer Science ETDs

Understanding the performance of parallel and distributed programs remains a focal point in determining how compute systems can be optimized to achieve exascale performance. Lightweight, statistical models allow developers to both characterize and predict performance trade-offs, especially as HPC systems become more heterogeneous with many-core CPUs and GPUs. This thesis presents a lightweight, statistical modeling approach of performance variation which leverages extreme value theory by focusing on the maximum length of distributed workload intervals. This approach was implemented in MPI and evaluated on several HPC systems and workloads. I then present a performance model of partitioned communication which also uses …

Advanced Parallel Algorithms In Computational Electromagnetics, Shu Wang

Electrical and Computer Engineering ETDs

The rapid development of high performance computing has pushed the computational electromagnetic(CEM) towards high accuracy, high fidelity and extreme computational scales. There is a great need for existing CEM solvers to have enhanced parallelism and scaling capability. The purpose of this dissertation is to investigate advanced parallel algorithms for both frequency and time domain solvers.

In frequency domain, this work first develop the underpinnings of parallel preconditioning technique and high-order transmission condition in the context of multi-solver scheme. The result is a computing resource-aware and implementation wise compact solver. Then this work targeted at developing efficient algorithms for cases where …

Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann

Mathematics & Statistics ETDs

This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements …

Fluid Transport In Porous Media For Engineering Applications, Eric M. Benner

Chemical and Biological Engineering ETDs

This doctoral dissertation presents three topics in modeling fluid transport through porous media used in engineering applications. The results provide insights into the design of fuel cell components, catalyst and drug delivery particles, and aluminum- based materials. Analytical and computational methods are utilized for the modeling of the systems of interest. Theoretical analysis of capillary-driven transport in porous media show that both geometric and evaporation effects significantly change the time dependent behavior of liquid imbibition and give a steady state flux into the medium. The evaporation–capillary number is significant in determining the time-dependent behavior of capillary flows in porous media. …

Adaptive Parallelism For Coupled, Multithreaded Message-Passing Programs, Samuel K. Gutiérrez

Computer Science ETDs

Hybrid parallel programming models that combine message passing (MP) and shared- memory multithreading (MT) are becoming more popular, especially with applications requiring higher degrees of parallelism and scalability. Consequently, coupled parallel programs, those built via the integration of independently developed and optimized software libraries linked into a single application, increasingly comprise message-passing libraries with differing preferred degrees of threading, resulting in thread-level heterogeneity. Retroactively matching threading levels between independently developed and maintained libraries is difficult, and the challenge is exacerbated because contemporary middleware services provide only static scheduling policies over entire program executions, necessitating suboptimal, over-subscribed or under-subscribed, configurations. In …

Multi-Resolution Analysis Of Large Molecular Structures And Interactions, Kasra Manavi

Computer Science ETDs

Simulation of large molecular structures and their interactions has become a major component of modern biomolecular research. Methods to simulate these type of molecules span a wide array of resolutions, from all atom molecular dynamics to model interaction energetics to systems of linear equations to evaluate population kinetics. In recent years, there has been an acceleration of molecular structural information production, primarily from x-ray crystallography and electron microscopy. This data has provided modelers the ability to produce better representations of these molecular structures. The purpose of this research is to take advantage of this information to develop multi-resolution models for …

Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe

Shared Knowledge Conference

Chemical Reaction Networks (CRNs) are a popular tool in the chemical sciences for providing a means of analyzing and modeling complex reaction systems. In recent years, CRNs have attracted attention in the field of molecular computing for their ability to simulate the components of a digital computer. The reactions within such networks may occur at several different scales relative to one another – at rates often too difficult to directly measure and analyze in a laboratory setting. To facilitate the construction and analysis of such networks, we propose a reduced order model for simulating such networks as a system of …

Distributed Knowledge Discovery For Diverse Data, Hossein Hamooni

Computer Science ETDs

In the era of new technologies, computer scientists deal with massive data of size hundreds of terabytes. Smart cities, social networks, health care systems, large sensor networks, etc. are constantly generating new data. It is non-trivial to extract knowledge from big datasets because traditional data mining algorithms run impractically on such big datasets. However, distributed systems have come to aid this problem while introducing new challenges in designing scalable algorithms. The transition from traditional algorithms to the ones that can be run on a distributed platform should be done carefully. Researchers should design the modern distributed algorithms based on the …

Special Set Linear Algebra And Special Set Fuzzy Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book for the first time introduces the notion of special set linear algebra and special set fuzzy linear algebra. This is an extension of the book set linear algebra and set fuzzy linear algebra. These algebraic structures basically exploit only the set theoretic property, hence in applications one can include a finite number of elements without affecting the systems property. These new structures are not only the most generalized structures but they can perform multi task simultaneously; hence they would be of immense use to computer scientists. This book has five chapters. In chapter one the basic concepts about …