Review 20.3 for symplectic integrator. This week's assignment is fairly straightforward. This page provides some more detailed information on force softening.

The state of the art in N-body simulations is the P3M method, which models interactions at close range using a particle-particle model, and longer range interactions on a mesh. The method divides the space into a nested family of 8^n adjacent cubes (that is, each parent has 8 children), and each cell integration selects the necessary resolution for more distant parts of the mesh. Finally, when a particle changes the cell it's in, an efficient way of keeping track is needed. As you can imagine, this is a quite sophisticated algorithm! The astrophysics course AY190 covers it, if you're interested. Otherwise, just have nightmares about coding one.