This research has worked to develop a general computer implementation for symplectic algorithms applied to the N-body problem. A program was written to evolve an arbitra[...]

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[...]

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

ABSTRACTQIANG SHI. A convertible-bond-pricing method based on bond prices on markets.(Under the direction of DR. YOU-LAN ZHU)This thesis is devoted to evaluating two-fact[...]

For approximating the solution of partial differential equations (PDE), meshless methods have been introduced to alleviate the difficulties arising in mesh generation usi[...]

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 [...]

We develop numerical methods for analysis of fourth-order partial differential equations on domains with angular corners. For the finite element analysis of fourth-order [...]

For the last several decades, the Finite Element Method (FEM) has been a powerful tool in solving challenging science and engineering problems, especially when solution d[...]

The design basis functions in IGA are refined and enhanced by extra enrichment functions and various local refinements with the use of partition of unity (PU) functions w[...]