2. 2. 2 Spatial Resolution of a Simulation Domain

In order to find simple basis functions of a simulation domain, the simulation domain is tessellated into elements of a simple geometrical archetype [31], for instance into triangles, where single shape functions can be defined. In this section the tesselation of the simulation domain is considered, while the next section shows the construction of the basis functions on the tesselation.

The process of tesselation of a continuous domain, which is usually a partial set of $\mathcal{R}^2$ or $\mathcal{R}^3$ with a finite volume is usually performed by methods which are referred to as meshing or gridding. The main aim of these methods is to tessellate the given simulation domain into a number of subdomains. In most cases, the subdomains of the tesselation are simplices [64].

Such methods are also used in other fields of computer science such as visualization or computer games. In both fields, the main focus is put on the optimization of the visual appearance. In many cases only the surfaces of the respective objects are required.

It has to be stated that this field suffers from many unsolved problems and the tesselation of some simple domains as well as local refinement [65] turns out to be difficult and impossible in some cases. However, these problems mainly occur in three-dimensional simulation domains, whereas for two-dimensional domains the tesselation is rather straight forward.