This paper presents a computational platform for dynamic security assessment (DSA) of large electricity grids, developed as part of the iTesla project. It leverages high performance computing to analyze large power systems, with many scenarios and possible contingencies, thus paving the way for pan-European operational stability analysis. The results of the DSA are summarized by decision trees of 11 stability indicators. The platform's workflow and parallel implementation architecture is described in detail, including the way commercial tools are integrated into a plug-in architecture. A case study of the French grid is presented, with over 8000 scenarios and 1980 contingencies. Performance data of the case study (using 10 000 parallel cores) is analyzed, including task timings and data flows. Finally, the generated decision trees are compared with test data to quantify the functional performance of the DSA platform.