N-body simulation based on the Particle Mesh method using multigrid schemes

Through the last decades multigrid methods have been used extensively in the solution of large sparse linear systems derived from the discretization of Partial Differential Equations in two or three space variables, subject to a variety of boundary conditions. Due to their efficiency and convergence behavior, multigrid methods are used in many scientific fields as solvers or preconditioners. Herewith, we propose a new algorithm for N-body simulation, based on the V-Cycle multigrid method in conjunction with Generic Approximate SParse Inverses (GenAspI). The N-body problem chosen is in toroidal 3D space and the bodies are subject only to gravitational forces. In each time step, a large sparse linear system is solved to compute the gravity potential at each nodal point in order to interpolate the solution to each body and through the velocity Verlet method compute the new position, velocity and acceleration of each respective body. Moreover, a parallel version of the multigrid algorithm with a truncated approach in the parallel levels is utilized for the fast solution of the linear system. Furthermore parallel results are provided which depict the efficiency and performance for the proposed multigrid N-body scheme.