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Evaluation of pair potentials is critical in a number of areas of physics.The classicalN-body problem has its root in evaluating the Laplace potential,and has spawned tree-algorithms, the fast multipole method (FMM), as well askernel independent approaches. Over the years, FMM for Laplace potential hashad a profound impact on a number of disciplines as it has been possible todevelop highly scalable parallel algorithm for these potential evaluators. Thisis in stark contrast to parallel algorithms for the Helmholtz (oscillatory)potentials. The principal bottleneck to scalable parallelism are operationsnecessary to traverse up, across and down the tree, affecting both computationand communication. In this paper, we describe techniques to overcomebottlenecks and achieve high performance evaluation of the Helmholtz potentialfor a wide spectrum of geometries. We demonstrate that the resultingimplementation has a load balancing effect that significantly reduces thetime-to-solution and enhances the scale of problems that can be treated usingfull wave physics.

High Performance Evaluation of Helmholtz Potentials using the Multi-Level Fast Multipole Algorithm