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Commit fe92c7d0 authored by Matthieu Schaller's avatar Matthieu Schaller
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Complete the discussion of the truncated MAC estimator

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1 merge request!1077Improved multipole acceptance criterion (MAC)
...@@ -189,7 +189,25 @@ f_{\rm MAC}(r) = ...@@ -189,7 +189,25 @@ f_{\rm MAC}(r) =
\right. \right.
\label{eq:fmm:f_mac} \label{eq:fmm:f_mac}
\end{align} \end{align}
This esimator is shown as a dot-dashed line on Since it is made of constants and even powers of the distance,
Fig. \ref{fig:fmm:mac_potential} and obeys the relation $f_{\rm SWIFT}(r) computin this term is much cheaper than the true forces. This
\leq f_{\rm MAC}(r) \leq 1/r^2$, with $f_{\rm SWIFT}(r)$ the true esimator is shown as a dot-dashed line on
truncated and softened forces (green line). 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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