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SWIFT
SWIFTsim
Commits
10a76254
Commit
10a76254
authored
Jun 21, 2018
by
Matthieu Schaller
Browse files
More references in FMM theory document
parent
88831396
Changes
2
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theory/Multipoles/bibliography.bib
View file @
10a76254
...
...
@@ -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
View file @
10a76254
...
...
@@ -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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