Geant4 offers a variety of Runge-Kutta methods to integrate the motion of charged particles in a non-uniform electromagnetic field. In GeantV adapted RK methods are being vectorised to handle multiple tracks efficiently. Integration is used for the motion of charged particle and to identify the intersection point between the curved track and the volume boundaries. Due to the large number of steps and the cost of the evaluations of the field, the integration and intersection are a performance critical part of detector simulation. So integration methods must provide adequate accuracy while take as little computation time as possible, and thus a minimum of calls to evaluate the EM field. Past GSoC work introduced new RK methods with an interpolation capability for intermediate points; optimally utilising this should reduce, potentially substantially, the number of field evaluations. The potential to create a vectorised version of leading embedded RK methods for a single track could provide benefits from vectorisation to Geant4 and to the portion of GeantV tracking which occurs in single track mode.
This project requires prior exposure to Numerical Analysis and familiarity with either C++, C or Java programming. Exposure to either numerical methods for solving Ordinary Differential equations (ODEs), vectorisation techniques or tools for analysing data such as R, numpy or ROOT will be valuable. Both programming skill and knowledge of numerical methods for ODEs will be improved by undertaking this project.