Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Keplerian-based Hamiltonian Splitting for Gravitational $N$-body
  Simulations   We developed a Keplerian-based Hamiltonian splitting for solving the
gravitational $N$-body problem. This splitting allows us to approximate the
solution of a general $N$-body problem by a composition of multiple,
independently evolved $2$-body problems. While the Hamiltonian splitting is
exact, we show that the composition of independent $2$-body problems results in
a non-symplectic non-time-symmetric first-order map. A time-symmetric
second-order map is then constructed by composing this basic first-order map
with its self-adjoint. The resulting method is precise for each individual
$2$-body solution and produces quick and accurate results for near-Keplerian
$N$-body systems, like planetary systems or a cluster of stars that orbit a
supermassive black hole. The method is also suitable for integration of
$N$-body systems with intrinsic hierarchies, like a star cluster with
primordial binaries. The superposition of Kepler solutions for each pair of
particles makes the method excellently suited for parallel computing; we
achieve $\gtrsim 64\%$ efficiency for only $8$ particles per core, but close to
perfect scaling for $16384$ particles on a $128$ core distributed-memory
computer. We present several implementations in \texttt{Sakura}, one of which
is publicly available via the AMUSE framework.

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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat