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Low-Communication, Parallel Multigrid Algorithms For Elliptic Partial Differential Equations, Wayne Mitchell 2017 University of Colorado, Boulder

Low-Communication, Parallel Multigrid Algorithms For Elliptic Partial Differential Equations, Wayne Mitchell

Applied Mathematics Graduate Theses & Dissertations

When solving elliptic partial differential equations (PDE's) multigrid algorithms often provide optimal solvers and preconditioners capable of providing solutions with O(N) computational cost, where N is the number of unknowns. As parallelism of modern super computers continues to grow towards exascale, however, the cost of communication has overshadowed the cost of computation as the next major bottleneck for multigrid algorithms. Typically, multigrid algorithms require O((log P)^2) communication steps in order to solve a PDE problem to the level of discretization accuracy, where P is the number of processors. This has inspired the development of new algorithms ...


An Investigation Of The Accuracy Of Parallel Analysis For Determining The Number Of Factors In A Factor Analysis, Mandy Matsumoto 2017 Western Kentucky University

An Investigation Of The Accuracy Of Parallel Analysis For Determining The Number Of Factors In A Factor Analysis, Mandy Matsumoto

Honors College Capstone Experience/Thesis Projects

Exploratory factor analysis is an analytic technique used to determine the number of factors in a set of data (usually items on a questionnaire) for which the factor structure has not been previously analyzed. Parallel analysis (PA) is a technique used to determine the number of factors in a factor analysis. There are a number of factors that affect the results of a PA: the choice of the eigenvalue percentile, the strength of the factor loadings, the number of variables, and the sample size of the study. Although PA is the most accurate method to date to determine which factors ...


Shrinkage Function And Its Applications In Matrix Approximation, Toby Boas, Aritra Dutta, Xin Li, Katie Mercier, Eric Niderman 2017 University of Florida, Gainesville

Shrinkage Function And Its Applications In Matrix Approximation, Toby Boas, Aritra Dutta, Xin Li, Katie Mercier, Eric Niderman

Electronic Journal of Linear Algebra

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the shrinkage function are demonstrated in solving several well-known problems, together with a new result in matrix approximation.


Full Wave Modeling Of Ultrasonic Scattering Using Nystrom Method For Nde Applications, Praveen Gurrala, Kun Chen, Jiming Song, Ron Roberts 2017 Iowa State University

Full Wave Modeling Of Ultrasonic Scattering Using Nystrom Method For Nde Applications, Praveen Gurrala, Kun Chen, Jiming Song, Ron Roberts

Jiming Song

Approximate methods for ultrasonic scattering like the Kirchhoff approximation and the geometrical theory of diffraction (GTD) can deliver fast solutions with relatively small computational resources compared to accurate numerical methods. However, these models are prone to inaccuracies in predicting scattered fields from defects that are not very large compared to wavelength. Furthermore, they do not take into account physical phenomena like multiple scattering and surface wave generation on defects. Numerical methods like the finite element method (FEM) and the boundary element method (BEM) can overcome these limitations of approximate models. Commercial softwares such as Abaqus FEA and PZFlex use FEM ...


Fast Algorithms On Random Matrices And Structured Matrices, Liang Zhao 2017 The City University of New York

Fast Algorithms On Random Matrices And Structured Matrices, Liang Zhao

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

Randomization of matrix computations has become a hot research area in the big data era. Sampling with randomly generated matrices has enabled fast algorithms to perform well for some most fundamental problems of numerical algebra with probability close to 1. The dissertation develops a set of algorithms with random and structured matrices for the following applications: 1) We prove that using random sparse and structured sampling enables rank-r approximation of the average input matrix having numerical rank r. 2) We prove that Gaussian elimination with no pivoting (GENP) is numerically safe for the average nonsingular and well-conditioned matrix preprocessed with ...


High Performance Computation Of Cardiac Models In Real-Time Using Webgl, Abouzar Kaboudian, Flavio H. Fenton 2017 Georgia Institute of Technology

High Performance Computation Of Cardiac Models In Real-Time Using Webgl, Abouzar Kaboudian, Flavio H. Fenton

Biology and Medicine Through Mathematics Conference

No abstract provided.


A Large Reaction-Diffusion Model For Cell Polarization In Yeast, Marissa Renardy 2017 The Ohio State University

A Large Reaction-Diffusion Model For Cell Polarization In Yeast, Marissa Renardy

Biology and Medicine Through Mathematics Conference

No abstract provided.


Evolution Of Influenza H3n2: A Random Walk In High Dimensions, James R. Moore 2017 Emory University

Evolution Of Influenza H3n2: A Random Walk In High Dimensions, James R. Moore

Biology and Medicine Through Mathematics Conference

No abstract provided.


Building And Validating A Model For Investigating The Dynamics Of Isolated Water Molecules, Grant Cates 2017 Linfield College

Building And Validating A Model For Investigating The Dynamics Of Isolated Water Molecules, Grant Cates

Senior Theses

Understanding how water molecules behave in isolation is vital to understand many fundamental processes in nature. To that end, scientists have begun studying crystals in which single water molecules become trapped in regularly occurring cavities in the crystal structure. As part of that investigation, numerical models used to investigate the dynamics of isolated water molecules are sought to help bolster our fundamental understanding of how these systems behave. To that end, the efficacy of three computational methods—the Euler Method, the Euler-Aspel Method and the Beeman Method—is compared using a newly defined parameter, called the predictive stability coefficient ρ ...


Application Of Symplectic Integration On A Dynamical System, William Frazier 2017 East Tennessee State University

Application Of Symplectic Integration On A Dynamical System, William Frazier

Electronic Theses and Dissertations

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic ...


Accuracy And Stability Of Integration Methods For Neutrino Transport In Core Collapse Supernovae, Kyle A. Gregory 2017 kgrego12

Accuracy And Stability Of Integration Methods For Neutrino Transport In Core Collapse Supernovae, Kyle A. Gregory

University of Tennessee Honors Thesis Projects

No abstract provided.


Electrodynamical Modeling For Light Transport Simulation, Michael G. Saunders 2017 East Tennessee State University

Electrodynamical Modeling For Light Transport Simulation, Michael G. Saunders

Undergraduate Honors Theses

Modernity in the computer graphics community is characterized by a burgeoning interest in physically based rendering techniques. That is to say that mathematical reasoning from first principles is widely preferred to ad hoc, approximate reasoning in blind pursuit of photorealism. Thereby, the purpose of our research is to investigate the efficacy of explicit electrodynamical modeling by means of the generalized Jones vector given by Azzam [1] and the generalized Jones matrix given by Ortega-Quijano & Arce-Diego [2] in the context of stochastic light transport simulation for computer graphics. To augment the status quo path tracing framework with such a modeling technique ...


Hawking Radiation And Classical Tunneling: A Numerical Study, Dmitriy Zhigunov 2017 College of William and Mary

Hawking Radiation And Classical Tunneling: A Numerical Study, Dmitriy Zhigunov

Undergraduate Honors Theses

Unruh [1] demonstrated that black holes have an analogy in acoustics. Under this analogy the acoustic event horizon is defined by the set of points in which the local background flow exceeds the local sound speed. In past work [2], we demonstrated that under a white noise source, the acoustic event horizon will radiate at a thermal spectrum via a classical tunneling process. In this work, I summarize the theory presented in [2] and nondimensionalize it in order to reduce the dynamical equations to one parameter, the coupling coefficient η2. Since η2 is the sole parameter of the system, we ...


Plateau Potential Fluctuations And Intrinsic Membrane Noise, Daniel Scott Borrus 2017 College of William and Mary

Plateau Potential Fluctuations And Intrinsic Membrane Noise, Daniel Scott Borrus

Undergraduate Honors Theses

This thesis focuses on subthreshold membrane potential fluctuations in the plateau potentials of bistable neurons. Research involved with plateau potentials typically finds one of the resting membrane potentials to be more susceptible to voltage fluctuations. This difference in the amplitude of the membrane potential fluctuations is most often attributed to the voltage-dependent membrane conductance. Occasionally, however, the typically quieter resting membrane potential exhibits larger voltage fluctuations than the expected one. It has been proposed that this increased membrane potential noise is the result of the stochastic gating of the voltage-gated ion channels. In this thesis, we use a simple bistable ...


Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker 2017 Cedarville University

Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker

The Research and Scholarship Symposium

Nation-building modeling is an important field of research given the increasing number of candidate nations and the limited resources available. A modeling methodology and a system of differential equations model are presented to investigate the dynamics of nation-building. The methodology is based upon parameter identification techniques applied to a system of differential equations, to evaluate nation-building operations. Data from Operation Iraqi Freedom (OIF) and Afghanistan are used to demonstrate the validity of different models as well as the comparison of models.


Testing The Consistency Of Nested Logit Models With Utility Maximization, Joseph A. Herriges, Catherine L. Kling 2017 Iowa State University

Testing The Consistency Of Nested Logit Models With Utility Maximization, Joseph A. Herriges, Catherine L. Kling

Catherine Kling

The Nested Multinomial Logit (NMNL) model is used extensively in modeling consumer choices among discrete alternatives when the number of alternatives is large. Unfortunately, applied researchers often find that estimated NMNL models fail to meet the Daly-ZacharyMcFadden (DZM) sufficient conditions for consistency with stochastic utility maximization. Borsch-Supan (1990) provides a relaxed set of conditions to test for consistency. While these conditions are increasingly cited, they are seldom tested. This paper corrects and extends BorschSupan's Theorem 2, providing simple necessary conditions on first, second, and third derivatives of choice probabilities and a graph oft he bounds they place on dissimilarity ...


Steady State Probabilities In Relation To Eigenvalues, Pellegrino Christopher 2017 Liberty University

Steady State Probabilities In Relation To Eigenvalues, Pellegrino Christopher

The Kabod

By using the methods of Hamdy Taha, eigenvectors can be used in solving problems to compute steady state probabilities, and they work every time.


Mri-Based Susceptibility Mapping For In-Vivo Iron And Blood Oximetry Measurements, Hannah Erdevig 2017 University of Colorado, Boulder

Mri-Based Susceptibility Mapping For In-Vivo Iron And Blood Oximetry Measurements, Hannah Erdevig

Undergraduate Honors Theses

MRI is increasingly used in mapping tissue susceptibility to identify cerebral microbleeds associated with traumatic brain injury and pathological iron deposits associated with neurodegenerative diseases such as Parkinson's and Alzheimer's disease [1,2]. Accurate measurement is important for determining oxygen and iron content in blood vessels and tissue in the brain, which are in turn used for noninvasive clinical diagnosis and treatment assessments. Magnetic field distortions with a resolution of a few parts per billion can be measured using MRI phase maps. The field distortion map can then be inverted to obtain a quantitative susceptibility map. The primary ...


A Numerical Study Of Construction Of Honey Bee Comb, Pamela Guerrero, Pamela C. Guerrero 2017 Murray State University

A Numerical Study Of Construction Of Honey Bee Comb, Pamela Guerrero, Pamela C. Guerrero

Murray State Theses and Dissertations

We use finite difference methods in the treatment of an existing system of partial differential equations that captures the dynamics of parallel honeycomb construction in a bee hive. We conduct an uncertainty analysis by calculating the partial rank correlation coefficient for the parameters to find which are most important to the outcomes of the model. We then use an eFAST method to determine both the individual and total sensitivity index for the parameters. Afterwards we examine our numerical model under varying initial conditions and parameter values, and compare ratios found from local data with the golden mean by fitting images ...


A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang 2017 University of Kentucky

A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

Theses and Dissertations--Mechanical Engineering

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model ...


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