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I present the algorithm, theory and numerical experiments for the implementation of an N-body algorithm. It scales linearly in the number of particles for the computational effort per time step, independent of particle clustering. The resolution is fully adaptive, with a typical smoothing length comparable to the local interparticle separation. This is accomplished through the use of a structured dynamical coordinate system, which adjusts itself to the local density distribution. The gravity is solved on this adaptive moving mesh. For the Poisson solver a multigrid iteration scheme is used. The algorithm is fully vectorizable and parallelizable and is straightforward to implement on distributed memory massively parallel computers. Periodic or isolated boundary conditions can be used. Applications to the problem of large scale structure formation are shown. Quantitative experimental and theoretical comparisons with other N-body methods are studied, measuring the relative speed and accuracy.
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