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High Order H(div) Discontinuous Galerkin Methods for MHD Equations
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...
High-order integral equations for electromagnetic problems in layered media with applications in biology and solar cells
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...
IMAGE CHARGE SOLVATION MODEL (ICSM) FOR SIMULATING BIOMOLECULES AND KCSA ION-CHANNELS
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...
Path Integral Methods Using Feynman-Kac Formula and Reflecting Brownian Motions for Neumann and Robin Problems
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...