Summary

Building Information Modeling (BIM) was introduced in order to modelthe life cycle of buildings and infrastructures, and to make them available for questions at a higher level. Demanding processes like environment simulations or city and spatial planning, however, must consider in the sense of Geographic Information Systems (GIS), starting from the micro level of single buildings, also quarters, whole cities and regions. Only then can the dynamics and the influence of climate- and environment-related quantities be simulated in different scales. The aim of this proposal is the conception and making available of methods for supporting distributed simulations of scale-overlapping processes in the BIM/GIS context. Hereby, novel mathematical and information-technological methods shall come to their application. More explicitly, processes on finite topologies are to be described in a mathematically sound way and run as efficiently as possible using graph theory and p-adic analysis. Regarding implementations, algorithms and partitionable data structures are to be provided which are suitable for a distributed processing also across levels of detail or scale, respectively. Using topology as a scale-free perspective on describing processes, thought-provoking impulses for new generations of data modeling standards like IFC and CityGML are to be given. Finally, the practicability of the developped concepts and software are to be demonstrated on a typical process like the heat propagation within an integrated 3D city and building model.