Grav-Sim

The following results are measurements of elapsed time vs total energy error for the full range of accelerators (tree codes or brute-force) available in Grav-Sim. The tests were conducted according to the following criteria:

A standard Plummer model was used in each test, with either 1,000, 10,000 or 100,000 bodies.
All calculations were done in IEEE standard double precision using the "GravSim" command-line simulator.
The default Hermite-6 integrator was used throughout at the default level 1.
The integrations were numeric-only with no analytic orbit detection.
Tests were performed in serial mode (i.e. one CPU only) to eliminate any effect due to the suitability or otherwise of each algorithm for parallelisation.
The tree-code tests were done with the opening angle "theta" set to the relatively wide default value of 0.75.
Timings were taken on a Pentium dual-core CPU @ 2.6 GHz with 1Gb RAM and running Windows XP.
No softening is used - just pure Newtonian gravity

1,000-body Plummer Model (To Simulated Time 1.0)

Time-Steps	Accelerator	Interactor	Space Divider	Elapsed Time	Energy Error
Individual	Barnes-Hut	Direct	Octree	5.5 seconds	0.455493 %
Individual	Stadel*	Direct	KDTree	6.5 seconds	0.451888 %
Individual	Ridler**	Direct	Hilbert	5.4 seconds	0.438864 %
Individual	Dehnen	Pairwise	Octree	5.6 seconds	0.223357 %
Individual	Dehnen-Stadel*	Pairwise	KDTree	6.0 seconds	0.244912 %
Individual	Dehnen-Ridler**	Pairwise	Hilbert	5.8 seconds	0.411655 %
Individual	Brute-Force	N/A	N/A	5.8 seconds	0.315941 %
Shared	Barnes-Hut	Direct	Octree	17.3 seconds	0.031596 %
Shared	Stadel*	Direct	KDTree	22.4 seconds	0.038903 %
Shared	Ridler**	Direct	Hilbert	18.6 seconds	0.001052 %
Shared	Dehnen	Pairwise	Octree	14.0 seconds	0.382969 %
Shared	Dehnen-Stadel*	Pairwise	KDTree	17.7 seconds	0.124228 %
Shared	Dehnen-Ridler**	Pairwise	Hilbert	14.5 seconds	0.010016 %
Shared	Brute-Force	N/A	N/A	41.6 seconds	0.002367 %
Constant	Barnes-Hut	Direct	Octree	2 minutes 13 seconds	400.249 %
Constant	Stadel	Direct	KDTree	2 minutes 57 seconds	1.09441 %
Constant	Ridler*	Direct	Hilbert	1 minute 49 seconds	3.99687 %
Constant	Dehnen	Pairwise	Octree	1 minute 14.3 seconds	0.397287 %
Constant	Dehnen-Stadel*	Pairwise	KDTree	1 minute 54 seconds	0.101437 %
Constant	Dehnen-Ridler*	Pairwise	Hilbert	1 minute 18.4 seconds	0.013006 %
Constant	Brute-Force	N/A	N/A	4 minutes 0 seconds	2.91443 %
* - note the KDTree used here is unbalanced, unlike the one implemented by Joachim Stadel ** - experimental

10,000-body Plummer Model (To Simulated Time 0.1)

Time-Steps	Accelerator	Interactor	Space Divider	Elapsed Time	Energy Error
Individual	Barnes-Hut	Direct	Octree	43.9 seconds	0.003861 %
Individual	Stadel*	Direct	KDTree	82.1 seconds	0.007884 %
Individual	Ridler**	Direct	Hilbert	38.7 seconds	0.001642 %
Individual	Dehnen	Pairwise	Octree	54.1 seconds	0.018990 %
Individual	Dehnen-Stadel*	Pairwise	KDTree	80.4 seconds	0.000480 %
Individual	Dehnen-Ridler**	Pairwise	Hilbert	80.4 seconds	0.008884 %
Individual	Brute-Force	N/A	N/A	1 minute, 52 seconds	0.005719 %
Shared	Barnes-Hut	Direct	Octree	3 minutes, 58 seconds	0.000590 %
Shared	Stadel*	Direct	KDTree	3 minutes, 27 seconds	0.001791 %
Shared	Ridler**	Direct	Hilbert	4 minutes, 6 seconds	0.005514 %
Shared	Dehnen	Pairwise	Octree	2 minutes, 36 seconds	0.023204 %
Shared	Dehnen-Stadel*	Pairwise	KDTree	2 minutes, 28 seconds	0.011385 %
Shared	Dehnen-Ridler**	Pairwise	Hilbert	2 minutes, 49 seconds	0.014919 %
Shared	Brute-Force	N/A	N/A	33 minutes, 6 seconds	0.000178 %
Constant	Barnes-Hut	Direct	Octree	21 minutes, 26 seconds	0.166846 %
Constant	Stadel	Direct	KDTree	19 minutes, 0 seconds	0.169970 %
Constant	Ridler*	Direct	Hilbert	21 minutes, 21 seconds	13.7187 %
Constant	Dehnen	Pairwise	Octree	14 minutes, 22 seconds	0.023058 %
Constant	Dehnen-Stadel*	Pairwise	KDTree	14 minutes, 38 seconds	0.011628 %
Constant	Dehnen-Ridler*	Pairwise	Hilbert	15 minutes, 34 seconds	0.015594 %
Constant	Brute-Force	N/A	N/A	2 hours, 53 minutes	0.123633 %
* - note the KDTree used here is unbalanced, unlike the one implemented by Joachim Stadel ** - experimental

100,000-body Plummer Model (To Simulated Time 0.01)

Time-Steps	Accelerator	Interactor	Space Divider	Elapsed Time	Energy Error
Individual	Barnes-Hut	Direct	Octree	2 minutes, 50 seconds	0.000252 %
Individual	Stadel*	Direct	KDTree	5 minutes, 8 seconds	0.000064 %
Individual	Ridler**	Direct	Hilbert	2 minutes, 48 seconds	0.001275 %
Individual	Dehnen	Pairwise	Octree	3 minutes, 20 seconds	0.003910 %
Individual	Dehnen-Stadel*	Pairwise	KDTree	5 minutes, 28 seconds	0.001213 %
Individual	Dehnen-Ridler**	Pairwise	Hilbert	8 minutes, 4 seconds	0.021340 %
Individual	Brute-Force	N/A	N/A	1 hour, 2 minutes	0.000096 %
Shared	Barnes-Hut	Direct	Octree	29 minutes, 15 seconds	0.000209 %
Shared	Stadel*	Direct	KDTree	37 minutes, 38 seconds	0.000078 %
Shared	Ridler**	Direct	Hilbert	39 minutes, 56 seconds	0.001210 %
Shared	Dehnen	Pairwise	Octree	21 minutes, 23 seconds	0.003887 %
Shared	Dehnen-Stadel*	Pairwise	KDTree	29 minutes, 1 seconds	0.001164 %
Shared	Dehnen-Ridler**	Pairwise	Hilbert	29 minutes, 45 seconds	0.021235 %
Shared	Brute-Force	N/A	N/A	36 hours (est)
Constant	Barnes-Hut	Direct	Octree	3 hours, 1 minutes	0.000208 %
Constant	Stadel	Direct	KDTree	3 hours, 53 minutes	0.000077 %
Constant	Ridler*	Direct	Hilbert	4 hours, 5 minutes	0.001213 %
Constant	Dehnen	Pairwise	Octree	2 hours, 7 minutes	0.003887 %
Constant	Dehnen-Stadel*	Pairwise	KDTree	2 hours, 59 minutes	0.001162 %
Constant	Dehnen-Ridler*	Pairwise	Hilbert	2 hours, 59 minutes	0.021246 %
Constant	Brute-Force	N/A	N/A	9 days (est)
* - note the KDTree used here is unbalanced, unlike the one implemented by Joachim Stadel ** - experimental

Grav-Sim
Gravity simulation on a desktop computer

Gravity simulation on a desktop computer

1,000-body Plummer Model (To Simulated Time 1.0)

10,000-body Plummer Model (To Simulated Time 0.1)

100,000-body Plummer Model (To Simulated Time 0.01)