Scalability of the parallel MLFMA

This paper investigates the scalability of the parallel multilevel fast multipole algorithm (MLFMA). The scalability of a parallel algorithm is its ability to handle a larger problem on a proportionally larger parallel environment without loss of efficiency. It is demonstrated that this is closely related to the distribution of the workload among the different nodes: conventional spatial and hybrid partitioning techniques do not lead to a scalable algorithm, as opposed to the recently introduced hierarchical partitioning scheme. The repartitioning requirements for both the two- and three-dimensional case are investigated. It is shown how the hierarchical partitioning scheme can be combined with an asynchronous implementation that is suitable for scattering at multiple dielectric objects. A scalable open-source implementation in two dimensions is presented and the accurate scattering at a perfect electric conduction cylinder with a diameter of 1.2 million wavelengths is presented