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PkdGRAV2 is a high performance N-body treecode for self-gravitating astrophysical simulations. It is designed to run efficiently in serial and on a wide variety of parallel computers including both shared memory and message passing architectures. It can spatially adapt to large ranges in particle densities, and temporally adapt to large ranges in dynamical timescales. The code uses a non-standard data structure for efficiently calculating the gravitational forces, a variant on the k-D tree, and a novel method for treating periodic boundary conditions.
Pkdgrav3 is an 𝒪(N) gravity calculation method; it uses a binary tree algorithm with fifth order fast multipole expansion of the gravitational potential, using cell-cell interactions. Periodic boundaries conditions require very little data movement and allow a high degree of parallelism; the code includes GPU acceleration for all force calculations, leading to a significant speed-up with respect to previous versions (ascl:1305.005). Pkdgrav3 also has a sophisticated time-stepping criterion based on an estimation of the local dynamical time.
GENGA (Gravitational ENcounters with Gpu Acceleration) integrates planet and planetesimal dynamics in the late stage of planet formation and stability analyses of planetary systems. It uses mixed variable integration when the motion is a perturbed Kepler orbit and combines this with a direct N-body Bulirsch-Stoer method during close encounters. It supports three simulation modes: 1.) integration of up to 2048 massive bodies; 2.) integration with up to a million test particles; and 3.) parallel integration of a large number of individual planetary systems.