Browsing by Author "Cao, Yanzhao"

Now showing items 1-13 of 13

Analysis and finite element approximation for nonlinear problems in poroelasticity and bioconvection

Chen, Song (2013-04-23)

This dissertation is concerned with nonlinear systems of partial differential equation with solution dependent physical coefficients satisfying the Nemytskii assumption. Such equations arise from two important application ...

Analysis and Optimal control of deterministic Vector-Borne diseases model

Son, Hyunjin (2018-07-18)

In this dissertation, two systems of deterministic differential equations are introduced to study the transmission of vector-borne diseases between a host and a vector. The total population of the host and the vector are ...

Applications of Stochastic Gradient Descent for Optimization of Complex Systems with Uncertainty

Das, Somak (2021-07-27)

The Stochastic Gradient Descent (SGD) method in all its variations has gained popularity with the recent progress in Machine learning. In this dissertation we implement and analyze two modifications of the SGD method. In ...

Convergence Analysis and Numerical Simulation of Particle Swarm Optimization

Weerasinghe, Kariyawasam Ganesha (2017-04-21)

Nature, including mankind, loves to optimize and the world is far from being deterministic. Thus, stochastic optimization is an important and active area of research in applied mathematics. Inspired by the social behavior ...

Design and Analysis of Low-Cost X-Ray Imaging System Incorporating Add-On Mouse Rotation System in Pre-Clinical Research

Zhou, Huanyi (2022-07-21)

Computed tomography (CT) has become an essential tool in diagnostic and sports medicine. It is able to generate a three-dimensional rendering that can be used to interrogate a given region or desired structure from any ...

Efficient Numerical Algorithms for Solving Nonlinear Filtering Problems

Bao, Feng (2014-06-18)

Examples of nonlinear filtering problems arise in biology, mathematical finance, signal processing, image processing, target tracking and many engineering applications. Commonly used numerical simulation methods are the ...

Experimental and theoretical characterization of thermal behavior of large format pouch type lithium-ion battery

Hu, Yang (2021-04-20)

Fundamental understanding of the heat generation process of lithium-ion batteries during operations is crucial for securing lifespan and safety by the cost-effective and efficient design of thermal management systems. Heat ...

Fast and well-conditioned boundary integral equation solvers for the numerical simulation of graphene plasmon

Chen, Yu (2018-07-18)

Surface plasmonic polaritons (SPPs) are evanescent electromagnetic waves coupled to free electron plasma oscillations. It was first observed in metallic gratings in 1902 by Wood. Modern plasmonics gained renewed interest ...

Mathematical and Numerical Analysis for Linear Peridynamic Boundary Value Problems

Wu, Hao (2017-04-26)

Peridynamics is motivated in aid of modeling the problems from continuum mechanics which involve the spontaneous discontinuity forms in the motion of a material system. By replacing differentiation with integration, ...

Model Order Reduction

Ciftci, Olcay (2014-11-24)

Model Order Reduction (MOR) is a wide area, and it has many techniques. In this thesis, we focus on Krylov subspaces method and Proper Orthogonal Decomposition (POD).We show some details about these two methods. A MATLAB ...

A Newton - Galerkin Finite Element Method to solve reduced dimensional Variable Density Flow and Solute Transport Equations using Proper Orthogonal Decomposition method

Ciftci, Olcay (2020-07-20)

The mathematical model of Variable Density Flow and Solute Transport (VDFST) is a time dependent, coupled and nonlinear dynamical system that is widely used to simulate seawater intrusion and related problems. The numerical ...

Numerical Modeling of Electromagnetic Wave Scattering by Layered Random Surfaces

Ulmer, Kelsey (2020-12-01)

We present an efficient numerical method for modeling the scattering of electromagnetic fields by a multiply layered medium with random interfaces. We propose a combination of the Monte Carlo-Transformed Field Expansion ...

Probabilistic schemes for semi-linear nonlocal diffusion equations with application in predicting runaway electron dynamics

Yang, Minglei (2019-12-05)

In this work, we focus on developing and analyzing novel probabilistic numerical approaches for solving several types of semi-linear nonlocal diffusion equations in both unbounded and bounded high dimensional spaces. First, ...