Automatic Tuning of the Fast Multipole Method Based on Integrated Performance Prediction

The Fast Multipole Method (FMM) is an efficient, widely used method for the solution of N-body problems. One of the main data structures is a hierarchical tree data structure describing the separation into near-field and far-field particle interactions. This article presents a method for automatic tuning of the FMM by selecting the optimal FMM tree depth based on an integrated performance prediction of the FMM computations. The prediction method exploits benchmarking of significant parts of the FMM implementation to adapt the tuning to the specific hardware system being used. Furthermore, a separate analysis phase at runtime is used to predict the computational load caused by the specific particle system to be computed. The tuning method was integrated into an FMM implementation. Performance results show that a reliable determination of the tree depth is achieved, thus leading to minimal execution times of the FMM algorithm.