Algorithmique hiérarchique parallèle haute performance pour les problèmes à N-corps. (High performance parallel hierarchical algorithmic for N-body problems)

This thesis focuses on the Fast Multipole Method which hierarchically solves the N-body problem with a linear operation count for any given precision. When considering Laplace equation, we aim at treating efficiently all particle distributions that arise in astrophysics and in molecular dynamics. We first study two different expressions of the main operator (“multipole-to-local”) as well as the corresponding error bounds. For these two expressions, we present a matrix formulation whose implementation with BLAS routines (Basic Linear Algebra Subprograms) offers impressive runtime speedup. For the targeted precisions, this approach appears to outperform the existing enhancements (FFT, rotations and plane waves), in case of both uniform and non uniform distributions. In addition to a new octree data structure and to algorithmic improvements of the adaptive version, we have also efficiently parallelized our method for shared and distributed memory architectures. Finally, comparisons with specialized codes justify the interest of our code for astrophysical simulations.