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SWIFT
SWIFTsim
Commits
edf1eb93
Commit
edf1eb93
authored
5 years ago
by
Matthieu Schaller
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Be more explicit about the softened expressions in the theory document
parent
77463e70
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1 merge request
!1077
Improved multipole acceptance criterion (MAC)
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theory/Multipoles/potential_softening.tex
+10
-5
10 additions, 5 deletions
theory/Multipoles/potential_softening.tex
with
10 additions
and
5 deletions
theory/Multipoles/potential_softening.tex
+
10
−
5
View file @
edf1eb93
...
@@ -51,9 +51,10 @@ r^{-3} & \mbox{if} & r \geq H,
...
@@ -51,9 +51,10 @@ r^{-3} & \mbox{if} & r \geq H,
\end{align}
\end{align}
with
$
g
(
u
)
\equiv
f'
(
u
)/
u
=
-
21
u
^
5
+
90
u
^
4
-
140
u
^
3
+
84
u
^
2
-
14
$
. This last
with
$
g
(
u
)
\equiv
f'
(
u
)/
u
=
-
21
u
^
5
+
90
u
^
4
-
140
u
^
3
+
84
u
^
2
-
14
$
. This last
expression has the advantage of not containing any divisions or
expression has the advantage of not containing any divisions or
branching, making it faster to evaluate than the softened force
branching (besides the always necessary check for
$
r<H
$
), making it
derived from the
\cite
{
Monaghan1985
}
spline kernel. Note also, the
faster to evaluate than the softened force derived from the
useful expression for the norm of the forces:
\cite
{
Monaghan1985
}
spline kernel. Note also, the useful expression
for the norm of the forces:
\begin{align}
\begin{align}
|
\mathbf
{
\nabla
}
\varphi
(r,H)| =
|
\mathbf
{
\nabla
}
\varphi
(r,H)| =
\left\lbrace
\begin{array}
{
rcl
}
\left\lbrace
\begin{array}
{
rcl
}
...
@@ -68,8 +69,6 @@ resulting forces are shown on Fig. \ref{fig:fmm:softening} (for more
...
@@ -68,8 +69,6 @@ resulting forces are shown on Fig. \ref{fig:fmm:softening} (for more
details about how these are constructed see section 2
details about how these are constructed see section 2
of~
\cite
{
Price2007
}
). For comparison purposes, we also implemented the
of~
\cite
{
Price2007
}
). For comparison purposes, we also implemented the
more traditional spline-kernel softening in
\swift
.
more traditional spline-kernel softening in
\swift
.
\begin{figure}
\begin{figure}
\includegraphics
[width=\columnwidth]
{
potential.pdf
}
\includegraphics
[width=\columnwidth]
{
potential.pdf
}
\caption
{
The density (top), potential (middle) and forces (bottom)
\caption
{
The density (top), potential (middle) and forces (bottom)
...
@@ -81,3 +80,9 @@ more traditional spline-kernel softening in \swift.
...
@@ -81,3 +80,9 @@ more traditional spline-kernel softening in \swift.
potential at
$
r
=
H
$
to better highlight the differences in shapes.
}
potential at
$
r
=
H
$
to better highlight the differences in shapes.
}
\label
{
fig:fmm:softening
}
\label
{
fig:fmm:softening
}
\end{figure}
\end{figure}
Users specify the value of the Plummer-equivalent softening
$
\epsilon
_{
\rm
Plummer
}$
in the parameter file.
\subsubsection
{
Interaction of bodies with different softening lengths
}
\textcolor
{
red
}{
MORE WORDS HERE.
}
\\
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