Commit fe92c7d0 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Complete the discussion of the truncated MAC estimator

parent bfa215a1
......@@ -189,7 +189,25 @@ f_{\rm MAC}(r) =
\right.
\label{eq:fmm:f_mac}
\end{align}
This esimator is shown as a dot-dashed line on
Fig. \ref{fig:fmm:mac_potential} and obeys the relation $f_{\rm SWIFT}(r)
\leq f_{\rm MAC}(r) \leq 1/r^2$, with $f_{\rm SWIFT}(r)$ the true
truncated and softened forces (green line).
Since it is made of constants and even powers of the distance,
computin this term is much cheaper than the true forces. This
esimator is shown as a dot-dashed line on
Fig. \ref{fig:fmm:mac_potential} and obeys the relation $f_{\rm
SWIFT}(r) \leq f_{\rm MAC}(r) \leq 1/r^2$, with $f_{\rm SWIFT}(r)$
being the true truncated and softened norm of the gravity forces the
code solves for (green line). We use this expression in the multipole
acceptance criterion instead of the $1/|\mathbf{R}|$ term:
\begin{equation}
\tilde{E}_{BA,p} M_Bf_{\rm MAC}(|\mathbf{R}|) < \epsilon_{\rm FMM} \min_{a\in
A}\left(|\mathbf{a}_a|\right).
\label{eq:fmm:mac_f_mac}
\end{equation}
The same change is applied to the MAC used of the M2P kernel
(eq. \ref{eq:fmm:mac_m2p}). In the non-truncated un-softened case, this
expression reduces to \citep{Dehnen2014} one. Using this expression
instead of the simpler Newtonian one only makes a difference in
simulations where a lot of particles cluster below the scale of the
softening, which is often the case for hydrodynamical simulations
including radiative cooling processes. The use of this term over the
simpler $1/r^2$ estimator is a runtime parameter.
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