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Exascale systems are predicted to have approximately one billion cores,assuming Gigahertz cores. Limitations on affordable network topologies fordistributed memory systems of such massive scale bring new challenges to thecurrent parallel programing model. Currently, there are many efforts toevaluate the hardware and software bottlenecks of exascale designs. There istherefore an urgent need to model application performance and to understandwhat changes need to be made to ensure extrapolated scalability. The fastmultipole method (FMM) was originally developed for accelerating N-bodyproblems in astrophysics and molecular dynamics, but has recently been extendedto a wider range of problems, including preconditioners for sparse linearsolvers. It's high arithmetic intensity combined with its linear complexity andasynchronous communication patterns makes it a promising algorithm for exascalesystems. In this paper, we discuss the challenges for FMM on current parallelcomputers and future exascale architectures, with a focus on inter-nodecommunication. We develop a performance model that considers the communicationpatterns of the FMM, and observe a good match between our model and the actualcommunication time, when latency, bandwidth, network topology, and multi-corepenalties are all taken into account. To our knowledge, this is the firstformal characterization of inter-node communication in FMM, which validates themodel against actual measurements of communication time.

A Performance Model for the Communication in Fast Multipole Methods on HPC Platforms