Commit 10a76254 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

More references in FMM theory document

parent 88831396
......@@ -248,4 +248,33 @@ keywords = "adaptive algorithms"
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{Warren1995,
author = {{Warren}, M.~S. and {Salmon}, J.~K.},
title = "{A portable parallel particle program}",
journal = {Computer Physics Communications},
year = 1995,
month = may,
volume = 87,
pages = {266-290},
doi = {10.1016/0010-4655(94)00177-4},
adsurl = {http://adsabs.harvard.edu/abs/1995CoPhC..87..266W},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{Barnes1986,
author = {{Barnes}, J. and {Hut}, P.},
title = "{A hierarchical O(N log N) force-calculation algorithm}",
journal = {\nat},
keywords = {Computational Astrophysics, Many Body Problem, Numerical Integration, Stellar Motions, Algorithms, Hierarchies},
year = 1986,
month = dec,
volume = 324,
pages = {446-449},
doi = {10.1038/324446a0},
adsurl = {http://adsabs.harvard.edu/abs/1986Natur.324..446B},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
......@@ -15,12 +15,14 @@ collisionless dynamics, the particles are a mere Monte-Carlo sampling
of the underlying coarse-grained phase-space distribution which
justifies the use of approximate method to evaluate
Eq.~\ref{eq:fmm:n_body}. The \emph{Fast Multipole Method} (FMM)
\citep{Greengard1987, Cheng1999}, popularized in the field and adapted
specifically for gravity solvers by \cite{Dehnen2000, Dehnen2002}, is
an $\mathcal{O}(N)$ method designed to solve Eq.~\ref{eq:fmm:n_body}
by expanding the potential in Taylor series \emph{both} around
$\mathbf{x}_i$ and $\mathbf{x}_j$ and grouping similar terms
arising from nearby particles. \\
\citep{Greengard1987, Cheng1999}, popularized in astronomy and adapted
specifically for gravity solvers by \cite{Dehnen2000, Dehnen2002} (see
also \cite{Warren1995} for related ideas), is an $\mathcal{O}(N)$
method designed to solve Eq.~\ref{eq:fmm:n_body} by expanding the
potential in Taylor series \emph{both} around $\mathbf{x}_a$ and
$\mathbf{x}_b$ and grouping similar terms arising from nearby
particles. For comparison, a \cite{Barnes1986} tree-code expands the
potential only around $\mathbf{x}_b$.
\subsubsection{Double expansion of the potential}
......@@ -38,8 +40,8 @@ arising from nearby particles. \\
In what follows, we use the compact multi-index notation of
\cite{Dehnen2014} (repeated in appendix \ref{sec:multi_index_notation}
for completeness) to simplify expressions and ease
comparisons. $\mathbf{k}$, $\mathbf{m}$ and $\mathbf{n}$ are
for completeness) to simplify expressions and ease comparisons with
other published work. $\mathbf{k}$, $\mathbf{m}$ and $\mathbf{n}$ are
multi-indices and $\mathbf{r}$, $\mathbf{R}$, $\mathbf{x}$,
$\mathbf{y}$ and $\mathbf{z}$ are vectors, whilst $a$ and $b$ are
particle indices. Note also that we make no assumption on the specific
......
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