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[...]

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[...]

Microstructure present at the end of rolling and cooling operations controls the product properties. Therefore, control of grain size is an important characteristic in an[...]

We describe detailed high-resolution numerical simulations of a class of shock-induced reactive turbulent mixing layers, where the scalar mixing, flow dynamics and combus[...]

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

In this dissertation, we mainly discuss the image approximation methods to the reaction field and their applications to electrostatic interactions in molecular dynamics s[...]

Isogeometric analysis (IGA) is a framework bridging the gap between Computer Aided Design (CAD) and Finite Element Analysis (FEA). So it drastically reduces the error in [...]

Isogeometric analysis (IGA), introduced by Hughes, et al. [2,3], is a mathematical approach that combines Finite Element analysis (FEA) in conjunction with engineering de[...]

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

The use of nonconventional beam classes in turbulence applications is investigated. Through the study on pseudo-Bessel correlated beam propagation in the atmosphere, it i[...]