Fast Multipole Method for particle interactions: an open source parallel library component

Abstract

The fast multipole method is used in many scientific computing applications such as astrophysics, fluid dynamics, electrostatics and others. It is capable of greatly accelerating calculations involving pair-wise interactions, but one impediment to a more widespread use is the algorithmic complexity and programming effort required to implement this method. We are developing an open source, parallel implementation of the fast multipole method, to be made available as a component of the PETSc library. In this process, we also contribute to the understanding of how the accuracy of the multipole approximation depends on the parameter choices available to the user. Moreover, the proposed parallelization strategy provides optimizations for automatic data decomposition and load balancing.