ABSTRACT
In this paper we present some tasks within the simulation, supervision, and control of tunneling and the respective mathematical, especially algebraic and geometric, solution methods. On the one hand, this is challenging for mathematical research since it illustrates that mathematically involved problems appear in this important practical area. On the other hand, it shows the engineer that mathematics and software technology have quite a few tools at hand or under development that improve current engineering technologies. Not surprisingly, by the abstraction to mathematical problems, techniques from other areas become applicable (by generalizations or adaptations) to the specific needs in tunneling. Vice versa, new results obtained within the project stimulate research and development in theory as well as in other application domains.
