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Parameter studies behind the conserving tree code, as figures.

Companion of conserving_tree_code.py; each figure answers one question:

Source: examples/conserving_tree_code_studies.py. Run it yourself with python examples/conserving_tree_code_studies.py [--output examples/output] [--quick] (needs pip install "tree-d-3d[examples]").

Figures

Section titled “Figures”

the pair potential and field of the bare, Plummer and compact (smooth cloud) softening; why the far field of the compact one is exact.

the smoothstep weights of two neighbouring leaves across their edge and the derivative that enters the force.

field error, memberships per particle and energy error against the band width.

the cheapest (order, theta) reaching a given field error for the rectangle and the triangle truncation, with the M2L and near-field work counted.

energy error over a long Verlet run: no secular drift with smooth membership on fixed co-moving boxes.

where the field error sits, for hard and smooth membership (it is not concentrated at leaf edges, and blending does not change its distribution).

the size of the Phi grad w force term relative to the ordinary w G term, which is what restores the exact gradient.