We have developed a new parallel tree method which will be called the forest method hereafter. This new method uses the sectional Voronoi tessellation (SVT) for the domain decomposition. The SVT decomposes a whole space into polyhedra and allows their flat borders to move by assigning different weights. The forest method determines these weights based on the load balancing among processors by means of the over-load diffusion (OLD). Moreover, since all the borders are flat, before receiving the data from other processors, each processor can collect enough data to calculate the gravity force with precision. Both the SVT and the OLD are coded in a highly vectorizable manner to accommodate on vector parallel processors. The parallel code based on the forest method with the Message Passing Interface is run on various platforms so that a wide portability is guaranteed. Extensive calculations with 15 processors of Fujitsu VPP300/16R indicate that the code can calculate the gravity force exerted on 10^5 particles in each second for some ideal dark halo. This code is found to enable an N-body simulation with 10^7 or more particles for a wide dynamic range and is therefore a very powerful tool for the study of galaxy formation and large-scale structure in the universe.
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