1.8 Overview of Theoretical Concepts

Figure 1.18: Overview of the mathematical concepts which have been introduced for the separation of a physical field domain into a base space and fiber space related to the concept of fiber bundles. The topological toolkit provides concepts to describe the internal structure of the cells of the cell complex to enable a generic data structure specification as well as generic traversal mechanisms. Concepts from computational topology such as chain and cochain complexes to obtain vector space structures within the tangent and cotangent space, are presented. Generic data access mechanisms are based on discrete field representations by cochains with their corresponding geometrical orientation and dimension.