Search results | J. Murrey Atkins Library

Title: High Order H(div) Discontinuous Galerkin Methods for MHD Equations
Author: Wu, Jian
Date Created: 2016
Subjects--Topical: Mathematics
Description: In this dissertation, we investigate the divergence-free discontinuous Galerkin method using the $\mathcal{H}$(\textbf{div}) basis, to solve the nonlinear ideal magnetohydrodynamics (MHD) equations. This is a novel approach to ensure the divergenc...

Title: High-order integral equations for electromagnetic problems in layered media with applications in biology and solar cells
Author: Zinser, Brian
Date Created: 2016
Subjects--Topical: Mathematics, Cytology, Electromagnetism
Description: We present two distinct mathematical models where high-order integral equations are applied to electromagnetic problems. The first problem is to find the electric potential in and around ion channels and Janus particles. The second problem is to f...

Title: IMAGE CHARGE SOLVATION MODEL (ICSM) FOR SIMULATING BIOMOLECULES AND KCSA ION-CHANNELS
Author: Baker, Katherine
Date Created: 2014
Subjects--Topical: Mathematics
Description: We present an order N method for calculating electrostatic interactions that has been integrated into the molecular dynamics portion of the TINKER Molecular Modeling package. This method, termed the Image-Charge Solvation Model (ICSM), and introdu...

Title: Inverse source problems for elliptic and parabolic equations
Author: Li, Qitong
Date Created: 2019
Subjects--Topical: Mathematics
Description: In this dissertation, we solve two inverse problems. The first one is the inverse source problem for the Helmholtz equation that governs the wave propagating in anisotropic media. The second one is to recover the initial condition for parabolic eq...

Title: Isogeometric collocation method for elasticity problems containing singularities
Author: Rattan, Puja
Date Created: 2016
Subjects--Topical: Mathematics
Description: Isogeometric analysis (IGA), introduced by Hughes, et al. [2,3], is a mathematical approach that combines Finite Element analysis (FEA) in conjunction with engineering design tools, such as CAD, which allows analysis, testing and redesign of struc...

Title: Numerical models of COVID-19
Author: Cung, Benjamin
Date Created: 2021
Subjects--Topical: Mathematics
Description: COVID-19 is an ongoing infectious disease where individuals progress through the following four stages: susceptible (S), exposed (E), infected (I), and recovered (R). The standard mathematical model for the spread of such diseases through a large ...

Title: Path Integral Methods Using Feynman-Kac Formula and Reflecting Brownian Motions for Neumann and Robin Problems
Author: Zhou, Yijing
Date Created: 2016
Subjects--Topical: Mathematics
Description: In this dissertation, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in 3d and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann and Robin b...

Title: RANDOMIZED NUMERICAL LINEAR ALGEBRA FOR KERNEL MATRIX COMPRESSION
Author: Maniar, Saumya Kandarp
Date Created: 2020
Subjects--Topical: Mathematics
Description: Matrices are used significantly as a medium to store data in many applications likeData Science, Computer Science, Statistics, and Applied Mathematics. Matrix computationslike matrix multiplication, matrix inversion, eigenvalue decomposition, sing...