Track finding and fitting are among the most complex parts of event reconstruction in high-energy physics, and usually dominate the computing time in a high luminosity environment. A central part of track reconstruction is the transport of a given track parametrisation (i.e. the parameter estimation and associated covariance matrices) through the detector, respecting the magnetic field setup and the traversed detector material. While track propagation in a sparse environment (e.g. tracking detector with layers) can be sufficiently well approximated by considering discrete interactions at several positions, the propagation in a material dense environment (e.g. calorimeters) is better served by a continuous application of material effects. Recently, a common tracking software project (Acts), originally from the Common Tracking code of the ATLAS experiment, has been developed in order to preserve the algorithmic concepts from the LHC start-up era and prepare them for the high luminosity era of the LHC and beyond. The software is designed in an abstract, detector independent way and prepared to allow highly parallelised execution of all involved software modules, including magnetic field access and alignment conditions. Therefore the propagation algorithm needs to be both flexible and adjustable. The implemented solution using a fourth order Runge-Kutta-Nyström integration and its extension with continuous material integration and eventual time propagation is presented and the navigation through different geometry setups involving different environments is demonstrated.
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