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N body problems (e.g. Newton's laws for one million stars in a globular cluster) can have succesful special purpose devices
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See GRAPE (GRAvity PipE) machine (Sugimoto et al. Nature 345 page 90,1990)
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Essential reason is that such problems need much less memory per floating point unit than most problems
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Globular Cluster: 10^6 computations per datum stored
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Finite Element Iteration: A few computations per datum stored
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Rule of thumb is that one needs one gigabyte of memory per gigaflop of computation in general problems and this general design puts most cost into memory not into CPU.
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Note GRAPE uses EXACTLY same parallel algorithm that one finds in the books (e.g. Solving Problems on Concurrent Processors) for N-body problems on classic distributed memory MIMD machines
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Secs 237.6
