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We can solve the small message size and poor communication/computation ratio by a simple change in algorithm which still preserves owner's compute rule.
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Reverse loops over i and j so that j is outer loop and i inner loop
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First for each i in processor, set MPGrav(i) = 0
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Now looping over j, increment each MPGrav(i) by contribution of those j that are local to processor
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Now fetch those j which are off processor and communicate as before M(j), Xuse(j)
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For this j, run over all i in processor, incrementing MPGrav(i) by the contribution of this j
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This version of algorithm reduces communication by a factor of the grain size n =N/Nproc
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and total communication overhead is approximately
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which is small for n > 100
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