Physical Sciences and Mathematics Commons^™

Hard And Soft Error Resilience For One-Sided Dense Linear Algebra Algorithms, Peng Du

Doctoral Dissertations

Dense matrix factorizations, such as LU, Cholesky and QR, are widely used by scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This dissertation develops fault tolerance algorithms for one-sided dense matrix factorizations, which handles Both hard and soft errors.

For hard errors, we propose methods based on diskless checkpointing and Algorithm Based Fault Tolerance (ABFT) to provide full matrix protection, including the left and right factor that are normally seen in …

Numerical Analysis Of First And Second Order Unconditional Energy Stable Schemes For Nonlocal Cahn-Hilliard And Allen-Cahn Equations, Zhen Guan

Doctoral Dissertations

This PhD dissertation concentrates on the numerical analysis of a family of fully discrete, energy stable schemes for nonlocal Cahn-Hilliard and Allen-Cahn type equations, which are integro-partial differential equations (IPDEs). These two IPDEs -- along with the evolution equation from dynamical density functional theory (DDFT), which is a generalization of the nonlocal Cahn-Hilliard equation -- are used to model a variety of physical and biological processes such as crystallization, phase transformations, and tumor growth. This dissertation advances the computational state-of-the-art related to this field in the following main contributions: (I) We propose and analyze a family of two-dimensional unconditionally energy …

Analysis Of Solvability And Applications Of Stochastic Optimal Control Problems Through Systems Of Forward-Backward Stochastic Differential Equations., Kirill Yevgenyevich Yakovlev

Doctoral Dissertations

A stochastic metapopulation model is investigated. The model is motivated by a deterministic model previously presented to model the black bear population of the Great Smoky Mountains in east Tennessee. The new model involves randomness and the associated methods and results differ greatly from the deterministic analogue. A stochastic differential equation is studied and the associated results are stated and proved. Connections between a parabolic partial differential equation and a system of forward-backward stochastic differential equations is analyzed.

A "four-step" numerical scheme and a Markovian type iterative numerical scheme are implemented. Algorithms and programs in the programming languages C and …

The Search For An Optimal Means Of Determining The Minmax Control Parameter Using Sensitivity Analysis, John Teye Brown

Doctoral Dissertations

The use of computational methods for design and simulation of control systems allows for a cost-effective trial and error approach. In this work, we are concerned with the robust, real-time control of physical systems whose state space is infinite-dimensional. Such systems are known as Distributed Parameter Systems (DPS). A body whose state is heterogeneous is a distributed parameter. In particular, this work focuses on DPS systems that are governed by linear Partial Differential Equations, such as the heat equation. We specifically focus on the MinMax controller, which is regarded as being a very robust controller. The mathematical formulation of the …

Mathematical Modeling Of Pipeline Features For Robotic Inspection, Yang Gao

Doctoral Dissertations

Underground pipeline systems play an indispensable role in transporting liquids in both developed and developing countries. The associated social and economic cost to repair a pipe upon abrupt failure is often unacceptable. Regular inspection is a preventative action that aims to monitor pipe conditions, catch abnormalities and reduce the chance of undesirable surprises. Robots with CCTV video cameras have been used for decades to inspect pipelines, yielding only qualitative information. It is becoming necessary and preferable for municipalities, project managers and engineers to also quantify the 3-D geometry of underground pipe networks. Existing robots equipped specialized hardware and software algorithms …

Near-Optimal Scheduling And Decision-Making Models For Reactive And Proactive Fault Tolerance Mechanisms, Nichamon Naksinehaboon

Doctoral Dissertations

As High Performance Computing (HPC) systems increase in size to fulfill computational power demand, the chance of failure occurrences dramatically increases, resulting in potentially large amounts of lost computing time. Fault Tolerance (FT) mechanisms aim to mitigate the impact of failure occurrences to the running applications. However, the overhead of FT mechanisms increases proportionally to the HPC systems' size. Therefore, challenges arise in handling the expensive overhead of FT mechanisms while minimizing the large amount of lost computing time due to failure occurrences.

In this dissertation, a near-optimal scheduling model is built to determine when to invoke a hybrid checkpoint …

Lifetime Prediction And Confidence Bounds In Accelerated Degradation Testing For Lognormal Response Distributions With An Arrhenius Rate Relationship, Steven Michael Alferink

Doctoral Dissertations

"Determining the lifetime of a product is an important component of quality assurance. Traditional life testing methods are infeasible for products that have been designed to have a very long lifetime because they require a lengthy testing period. An alternative method is accelerated degradation testing, where a response variable determining the usability of the product is measured over time under multiple accelerating stress levels. The resulting data are then used to predict the life distribution of the product under the design stress level. In this dissertation, several methods are proposed and studied for obtaining prediction bounds for the lifetime of …