Particle Methods

Abstract

The motion of stars in the universe is determined by a gravitational field, which itself depends on the position and mass of all stars. We shall use this interesting astrophysical problem, called the N-body problem, to introduce particle methods. Algorithmically, these methods are substantially different from grid-oriented computations for two reasons. First, grid operators are short-range operators: they act only on neighboring grid points. Standard particle methods, on the other hand, feature long-range interactions: all particles interact with all other particles. Second, the load balance of multicomputer computations based on particle methods depends on computed values. This contrasts with grid-oriented computations, where the load balance depends only on the amount of data. From our experience with LU-decomposition, which is based on long-range operators and whose load balance is data-dependent through pivoting, we already know that data-distribution strategies play an important role for particle methods on multicomputers. However, as for grid-oriented computations, the data distribution is also tied to the geometry of the problem.