More references in FMM theory document

theory/Multipoles/bibliography.bib

@@ -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}
+}
+
+
+
 

theory/Multipoles/fmm_summary.tex

@@ -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