How can we messure the accuracy of DS vs BH?

[Diego-Hinrichs]

Assuming a fixed value of N and a varying aperture factor in the Barnes-Hut algorithm, how can the accuracy be measured relative to the direct sum method?

[Hsin-Hung]

You can measure the accuracy or error in terms of the acceleration vector:

1. Compute the accelerations for all bodies using both the direct-sum (baseline) and the Barnes-Hut algorithm.
2. Use mean absolute deviation (MAD) to measure the differences in accelerations between the two methods. The relative magnitude of the errors can then be calculated as the ratio of MAD to the mean absolute acceleration from the direct-sum method.
3. You can run the simulation using the existing models or a Plummer model of unit mass, which is more common in testing n-body simulations.