An implementation of the Fast Multipole Algorithm for wave interaction problem on sparse arrays of floating bodies

Bruno Borgarino (1) , A. Babarit (1) , Pierre Ferrant (1)

1 LHEEA - Laboratoire de recherche en Hydrodynamique, Énergétique et Environnement Atmosphérique

This paper describes an implementation of the fast multipole algorithm using the free-surface Green’s function for ocean water waves. Its aim is to investigate different parameters of the fast multipole algorithm in order to efficiently carry out computations on sets of unknowns that are very inhomogeneously distributed in space. Some limits of the algorithm for this specific case are pointed out. Those limits are essentially due to slow convergence of the multipole expansion of the Green’s function. Eventually, a simplified algorithm for this specific application is described. The performance of the different algorithms is evaluated based on the computational time they require.

Mots clés: Fast multipole algorithm; Free-surface Green’s function; Multipole expansion; Sparse arrays; Wave energy conversion

Domaines: Mécanique des fluides [physics.class-ph]

Bruno Borgarino, A. Babarit, Pierre Ferrant. An implementation of the Fast Multipole Algorithm for wave interaction problem on sparse arrays of floating bodies. Journal of Engineering Mathematics, 2012, 77, pp.51-68. ⟨10.1007/s10665-012-9551-3⟩. ⟨hal-01145147⟩