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 repres[...]

We present an order N method for calculating electrostatic interactions that has been integrated into the molecular dynamics portion of the TINKER Molecular Modeling pack[...]

Matrices are used significantly as a medium to store data in many applications likeData Science, Computer Science, Statistics, and Applied Mathematics. Matrix computation[...]

Computational materials science plays a crucial role in advancing new and improved materials. To leverage the advantages of local and nonlocal methods and aid in the adva[...]

Background: The most common cause of sentinel events is ineffective communication among the healthcare team. Nurses’ documentation of communication, including documenting[...]

We introduce an efficient and accurate boundary element method for computing the electrostatic potential in closely-packed dielectric spheres and Janus particles. Close [...]

Diffusion is a scientific phenomena that can be modeled by partial differential equations. In this dissertation we first explore the development of equations for local, n[...]

In this dissertation, we investigate the divergence-free discontinuous Galerkin method using the $\mathcal{H}$(\textbf{div}) basis, to solve the nonlinear ideal magnetohy[...]

We present two distinct mathematical models where high-order integral equations are applied to electromagnetic problems. The first problem is to find the electric potenti[...]