No Mesh Radial Basis Function Method And The Incompressible Fluid Computing

In this thesis, we will report our results in the applied and numerical mathematics, including the raidal basis functions (RBF), numerical methods of the unsteady incompressible flows, joint density functional theory (JDFT) and the crystal growth model of linear macromolecules. In part I, we'll discuss the multiscale meshless method, the boundary knots methods (BKM), the meshless Petrov-Galerkin method (PG), meshless subdomain method and the meshless general domain decomposition methods. In part II, we'll discuss the inexact pressure boundary condition of the projection methods, the mass conserved numerical methods and meshless schemes for unsteady navier-stokes equations in vorticity formulation. In part III, we'll discuss the orbital-free joint density functional theory, the density functional theory not based on Born-Oppenheimer approximation, and crystal growth model of linear macromolecules.