Interaction Arrays

The two principal structures are cells or bins, and neighbor lists.

• Cells. Divide the domain into M=Mx*My cells, each a bit larger than the interaction cut-off distance. Construct two arrays. A Head-of-List array is M elements big. HoL(k) gives the first particle in cell k. The List array is a linked list containing all the other particles. That is, say HoL(k)=8. That means particle 8 is in cell k. Look in List(8)=12, say. So particle 12 is in cell k, and in List(12) is the next particle in cell k. This continues until List(.)=0, signifying the end of the list for that cell.

  Note that, when computing hte force, one needs only search over the cells on one side of the given cell, and only over particles "below" the given one.

• Neighbor List. Imagine two layers around each particle. The innermost layer has the cut-off distance as diameter, the outer layer is a coule of times as large. Two arrays are constructed. Point(k) gives the location of the first neighbor of particle k in the array List. Point(k+1) gives the first neighbor of particle k+1. The List array is about big.