Spectral Decomposition of Thermal Conductivity: Comparing Velocity Decomposition Methods in Homogeneous Molecular Dynamics Simulations

TL;DR

This paper compares three spectral thermal conductivity methods in molecular dynamics, introduces a new approach called HNEMA, and demonstrates significant computational efficiency improvements using GPU acceleration.

Contribution

The paper introduces HNEMA, a new spectral TC method, and provides a comprehensive comparison of existing methods, including a GPU-accelerated implementation.

Findings

All methods agree qualitatively except at optical phonon frequencies.

SHC and HNEMA converge faster than GKMA.

GPU implementation is over 1000 times faster than CPU.

Abstract

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.