Parallel multigrid summation for the N-body problem

An Θ(n) parallel multigrid summation method for the N -body problem is presented. The method works with vacuum or periodic boundary conditions. It is based on a hierarchical decomposition of computational kernels on multiple grids. For low accuracy calculations, appropriate for molecular dynamics, a sequential implementation is faster than both Fast Multipole and Particle Mesh Ewald (PME). Its parallel implementation is more scalable than PME and comparable to the fast multipole. The method can be combined with multiple time stepping integrators to produce a powerful simulation protocol for simulation of biological molecules and other materials. The parallel implementation is based on MPI, and is tested in a variety of clusters and shared memory computers. It is available as open-source in http://protomol.sourceforge.net. An auxiliary tool allows the automatic selection of optimal parameters for given molecular systems and accuracies required, and is available in http://mdsimaid.cse.nd.edu.