  The design of new applications, especially those based on heterogeneous
integration, must rely on detailed knowledge of material properties, such as
thermal conductivity (TC). To this end, multiple methods have been developed to
study TC as a function of vibrational frequency. Here, we compare three
spectral TC methods based on velocity decomposition in homogenous molecular
dynamics simulations: Green-Kubo modal analysis (GKMA), the spectral heat
current (SHC) method, and a method we propose called homogeneous nonequilibrium
modal analysis (HNEMA). First, we derive a convenient per-atom virial
expression for systems described by general many-body potentials, enabling
compact representations of the heat current, each velocity decomposition
method, and other related quantities. Next, we evaluate each method by
calculating the spectral TC for carbon nanotubes, graphene, and silicon. We
show that each method qualitatively agrees except at optical phonon
frequencies, where a combination of mismatched eigenvectors and a large density
of states produces artificial TC peaks for modal analysis methods. Our
calculations also show that the HNEMA and SHC methods converge much faster than
the GKMA method, with the SHC method being the most computationally efficient.
Finally, we demonstrate that our single-GPU modal analysis implementation in
GPUMD (Graphics Processing Units Molecular Dynamics) is over 1000 times faster
than the existing LAMMPS (Large-scale Atomic/Molecular Massively Parallel
Simulator) implementation on one CPU.
