  For the understanding of the origin and propagation of ultra-high energy
cosmic rays (UHECR) we developed a new approach to simulating UHECRs from an
arbitrary number of sources based on Monte Carlo technique. The method consists
of a combination of three steps. For distant sources we apply commonly accepted
parameterizations to calculate the contribution to the observed cosmic ray
flux. For sources of the local universe we use forward tracking through
realistic matter distributions and magnetic fields resulting from explicit
simulations of large-scale structure formation. From the calculations and the
forward tracking we generate maps of the probability to observe a particle with
a given energy from a discrete direction. To account for deflections in the
galactic field, these probability maps are transformed by matrices calculated
from backtracking of antiparticles through field parameterizations. Based on
the combined probability maps, Monte Carlo production of individual UHECR data
is performed which are then used in comparisons with UHECR measurements. The
simulated UHECR data serves for optimizing the analysis techniques used in
UHECR measurements as well as for constraining the parameter space of the
underlying source and magnetic field models.
