A GPU-Accelerated Barycentric Lagrange Treecode

Abstract: We present an MPI + OpenACC implementation of the kernel-independent barycentric Lagrange treecode (BLTC) for fast summation of particle interactions on GPUs. The distributed memory parallelization uses recursive coordinate bisection for domain decomposition and MPI remote memory access to build locally essential trees on each rank. The particle interactions are organized into target batch/source cluster interactions which efficiently map onto the GPU; target batching provides an outer level of parallelism, while the direct sum form of the barycentric particle-cluster approximation provides an inner level of parallelism. The GPU-accelerated BLTC performance is demonstrated on several test cases up to 1~billion particles interacting via the Coulomb potential and Yukawa potential.