  In this paper, we develop a highly efficient molecular dynamics code fully
implemented on graphics processing units for thermal conductivity calculations
using the Green-Kubo formula. We compare two different schemes for force
evaluation, a previously used thread-scheme where a single thread is used for
one particle and each thread calculates the total force for the corresponding
particle, and a new block-scheme where a whole block is used for one particle
and each thread in the block calculates one or several pair forces between the
particle associated with the given block and its neighbor particle(s)
associated with the given thread. For both schemes, two different classical
potentials, namely, the Lennard-Jones potential and the rigid-ion potential are
implemented. While the thread-scheme performs a little better for relatively
large systems, the block-scheme performs much better for relatively small
systems. The relative performance of the block-scheme over the thread-scheme
also increases with the increasing of the cutoff radius. We validate the
implementation by calculating lattice thermal conductivities of solid argon and
lead telluride.
