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Reduction of communication and efficient partitioning are key issues forachieving scalability in hierarchical $N$-Body algorithms like FMM. In thepresent work, we propose four independent strategies to improve partitioningand reduce communication. First of all, we show that the conventional wisdom ofusing space-filling curve partitioning may not work well for boundary integralproblems, which constitute about 50% of FMM's application user base. We proposean alternative method which modifies orthogonal recursive bisection to solvethe cell-partition misalignment that has kept it from scaling previously.Secondly, we optimize the granularity of communication to find the optimalbalance between a bulk-synchronous collective communication of the localessential tree and an RDMA per task per cell. Finally, we take the dynamicsparse data exchange proposed by Hoefler et al. and extend it to a hierarchicalsparse data exchange, which is demonstrated at scale to be faster than the MPIlibrary's MPI_Alltoallv that is commonly used.

Communication Reducing Algorithms for Distributed Hierarchical N-Body Problems with Boundary Distributions