Geometrical importance sampling in Geant4: from design to verification

The addition of flexible, general implementations of geometrical splitting and Russian Roulette, in combination called geometrical importance sampling, for variance reduction and of a scoring system, for controlling the sampling, are described. The efficiency of the variance reduction implementation is measured in a simulation of a typical benchmark experiment for neutron shielding. Using geometrical importance sampling a reduction of the computing time of a factor 89 compared to the analog calculation, for obtaining a neutron flux with a certain precision, was achieved for the benchmark application.