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It is found that the fast multipole algorithm (FMA), used to compute interactions between M bodies, can be used effectively in computing the electrostatic potential due to M bodies. This paper describes some of the few combinations of a parallel fast multipole algorithm and a capacitance solver. Another group has also combined the parallel FMA with a capacitance solver (Wang et al. 1996). The main difference between this and previous implementations of the fast multipole algorithm is the way parallelization was implemented. The current implementation performs well when compared to previous implementations. Other advances include precomputation, multiprocessor scalability, and a focus on data memory layout techniques. Many of these concepts that have been utilized in this implementation can be used in developing distributed memory implementations.