Provably scalable parallel multilevel fast multipole algorithm

In the parallel multilevel fast multipole algorithm (MLFMA), there exist two fundamental partitioning schemes for the distribution of the workload across processors: the spatial distribution of boxes and the spectral distribution of field samples. These two schemes can be combined in various manners. It is analytically and numerically shown that, in two dimensions, the recently introduced hierarchical approach yields a scalable parallel MLFMA. For the three-dimensional case, it is proved that only the combination of the hierarchical partitioning scheme and a two-dimensional partitioning of the field samples leads to a scalable algorithm