  We present the barycentric Lagrange dual tree traversal (BLDTT) fast
summation method for particle interactions. The scheme replaces well-separated
particle-particle interactions by adaptively chosen particle-cluster,
cluster-particle, and cluster-cluster approximations given by barycentric
Lagrange interpolation at proxy particles on a Chebyshev grid in each cluster.
The BLDTT is kernel-independent and the approximations can be efficiently
mapped onto GPUs, where target particles provide an outer level of parallelism
and source particles provide an inner level of parallelism. We present an
OpenACC GPU implementation of the BLDTT with MPI remote memory access for
distributed memory parallelization. The performance of the GPU-accelerated
BLDTT is demonstrated for calculations with different problem sizes, particle
distributions, geometric domains, and interaction kernels, as well as for
unequal target and source particles. Comparison with our earlier
particle-cluster barycentric Lagrange treecode (BLTC) demonstrates the superior
performance of the BLDTT. In particular, on a single GPU for problem sizes
ranging from $N$=1E5 to 1E8, the BLTC has $O(N\log N)$ scaling, while the BLDTT
has $O(N)$ scaling. In addition, MPI strong scaling results are presented for
the BLTC and BLDTT using $N$=64E6 particles on up to 32 GPUs.
