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...
We introduce an efficient and accurate boundary element method for computing the electrostatic potential in closely-packed dielectric spheres and Janus particles. Close physical proximity occurs in modeling molecular ion interactions or colloidal ...
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...
Background: The most common cause of sentinel events is ineffective communication among the healthcare team. Nurses’ documentation of communication, including documenting the notification of critical laboratory results (CLR), is important to ensur...
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...
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...
