We report on improvements made over the past two decades to our adaptivetreecode N-body method (HOT). A mathematical and computational approach to thecosmological N-body problem is described, with performance and scalabilitymeasured up to 256k ($2^{18}$) processors. We present error analysis andscientific application results from a series of more than ten 69 billion($4096^3$) particle cosmological simulations, accounting for $4 \times 10^{20}$floating point operations. These results include the first simulations usingthe new constraints on the standard model of cosmology from the Plancksatellite. Our simulations set a new standard for accuracy and scientificthroughput, while meeting or exceeding the computational efficiency of thelatest generation of hybrid TreePM N-body methods.
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