This thesis consists of two main parts --- a geometry description and a grid generation part. In an introduction we describe our motivation to consider these two questions. We describe our reference application --- the simulation of semiconductor technology --- and list the resulting requirements for grid generation and geometry description.
In the geometry description part we introduce a new concept of geometry description which is dual to the usual concept. In this concept, the geometry description consists of a set of functions. The first function allows to find the region containing a point, the other allow to compute intersections of simplices with boundary segments.
We show that this concept allows to create and modify geometry descriptions in a much more natural way than the standard geometry description based on a cell complex. Because of the natural functional behaviour of this alternative geometry description we call it contravariant geometry description or (shortly) cogeometry. The concept may be used for arbitrary space dimension.
In the grid generation part we consider different questions connected with 3D grid generation. We give a short overview over usual grid generation techniques, consider the requirements connected with the discretization of partial differential equations and the problems connected with anisotropy. Then we describe in detail the grid generation algorithm used in the package IBG.
At last, we consider the results of some example applications of the IBG package. They especially show the simplicity of creating complicate geometries using the contravariant geometry description.