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The O(N) hierarchical N-body algorithms and Massively Parallel Processors allow particle systems of 100 million particles or more to be simulated in acceptable time. We present a data-parallel implementation of Anderson's method and demonstrate both efficiency and scalability of the implementation on the Connection Machine CM-5/5E systems. The communication time for large particle systems amounts to about 10-25%, and the overall efficiency is about 35%. The evaluation of the potential field of a system of 100 million particles takes 3 minutes and 15 minutes on a 256 node CM-5E, giving expected four and seven digits of accuracy, respectively. The speed of the code scales linearly with the number of processors and number of particles.