Cosmic-ray particles with ultra-high energies (above $10^{18}$ eV) are studied through the properties of extensive air showers which they initiate in the atmosphere. The Pierre Auger Observatory detects these showers with unprecedented exposure and precision and the collected data are processed via dedicated software codes. Monte Carlo simulations of extensive air showers are very computationally expensive, especially at the highest energies and calculations are performed on the GRID for this purpose. The processing of measured and simulated data is described, together with a brief list of physics results which have been achieved.
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