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This paper introduces a communication scheme for distributed Fast Multipole Methods (FMMs) using MPI neighborhood collectives and uniform trees, designed for easy integration with existing shared-memory FMM implementations. The key innovation is leveraging uniform trees to simplify communication, allowing retention of shared-memory optimizations during distributed execution. Benchmarks on ARCHER2 show weak scaling up to 3.2e10 points on 512 nodes, demonstrating the method's scalability for large problems despite potential asymptotic limitations with non-uniform data.
Scale your existing shared-memory Fast Multipole Method to distributed memory with minimal code changes and still keep your shared-memory optimizations.
We present a simple hierarchical communication scheme for distributed Fast Multipole Methods (FMMs) based on MPI neighborhood collectives and uniform trees. The method targets the common case of extending an existing high-performance shared-memory uniform-tree FMM implementation to distributed memory with minimal redesign while preserving any shared memory optimizations optimizations. Benchmarks on the ARCHER2 supercomputer demonstrate that our method can scale to very large problem sizes, we demonstrate weak-scaling up to 3.2e10 uniformly distributed points on 512 nodes of the machine in our largest runs. Our simplifications based on uniform trees result in worse asymptotic scaling for non-uniform points, however we still obtain practically useful runtimes due to the ability to retain our shared memory optimizations.