RECFMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions (Communications in Computational Physics, 2018)
We present RECFMM, a program representation and implementation of a recursivescheme for parallelizing the adaptive fast multipole method (FMM) on shared-memorycomputers. It achieves remarkable high performance while maintaining mathematicalclarity and flexibility. The parallelization scheme signifies the recursion featurethat is intrinsic to the FMM but was not well exploited. The program modulesof RECFMM constitute a map between numerical computation components and advancedarchitecture mechanisms. The mathematical structure is preserved and exploited,neither obscured nor compromised, by parallel rendition of the recursion scheme.Modern software system – CILK in particular, which provides graph-theoretic optimalscheduling in adaptation to the dynamics in parallel execution – is employed.RECFMM supports multiple algorithm variants that mark the major advances withlow-frequency interaction kernels, and includes the asymmetrical version where thesource particle ensemble is not necessarily the same as the target particle ensemble.We demonstrate parallel performance with Coulomb and screened Coulomb interactions.