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Recently, we implemented a new parallel algorithm TPM (Xu 1994) to perform large N-body simulations on massively parallel supercomputers. Its performance on various types of massively supercomputers, including IBM SP2, Cray T3D, SGI Power Challenge, is discusses in terms of scalability, computation-to-communication ratio, wall-clock run time. A series of simulations using $256^3$ particles with boxsize of $80h^{-1}$Mpc were performed using various cosmological models (standard CDM, CDM+HDM, CDM+$\Lambda$). The spatial resolution in high density regions are expected to be $\approx 30 h^{-1}$kpc. Density profiles of the clusters of galaxies are examined in details, especially as a function of redshift. This can be directly compared with observational data. The structure of these clusters is also examined in small scales, indicating the site and time of galaxy formation in various cosmogony. The over-merging problem in the standard CDM cosmology is also discussed in comparison to that in other cosmological models.
