These forces determine new locations for the particles in each small time-step.
Forces can be either gravitational or coulombic.
The FMM has wide applications in astrophysics, molecular dynamics and computational fluid dynamics. Then, it performs two passes on the decomposition tree. The first pass starts at the leaves of the tree, computing multipole expansion coefficients for the gravitational field. It proceeds towards the root accumulating the multipole coefficients at intermediate tree-nodes. When the root is reached, the second pass starts.