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

Abstract

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 farfield 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.

Performance and Energy Evaluation of Parallel Particle Simulation Algorithms for Different Input Particle Data

“…In [9] a parallel sorting for the particles in the particle systems is presented which improves the locality of interacting particles for computation on a distributed memory architecture. A more application specific optimization has been presented in [10], which introduces 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.…”

Data‐aware tuning of scientific applications with model‐based autotuning

“…Especially for irregular applications, it is necessary to consider the input data because for these applications, the execution path often is heavily dependent on the data and, furthermore, the data layout in the memory cannot be predicted easily. Examples for such applications are as follows: sparse linear algebra, where the layout of the matrices may vary considerably and possibly a suitable storage format has to be selected ; particle simulations, where specific measures have to be taken to ensure an efficient execution with different particle distributions and particle distributions changing over the time ; stencil computations, especially on fractal structures which may grow unpredictably ; and neural simulations, where the behaviour of each neuron and its connections to other neurons may change over the simulation time . …”

“…Applications investigated less frequently are particle simulations , stencil computations and the visualisation of molecular dynamic processes . The particle simulation is a fast multipole method, which uses different methods for calculating interactions between particles of small and of long distance. The depth of the fast multipole method tree determines the numbers of both kinds of interactions.…”

“…However, influences on the performance arising from characteristics of the input data cannot be covered sufficiently with this approach as the input data are only known at the runtime of the applications. Data characteristics can be crucial for the execution behaviour especially of irregular applications, for example, particle methods with inhomogeneous particle distributions or linear algebra methods for sparse matrices .…”