  We present a tensor-decomposition method to solve the Boltzmann transport
equation (BTE) in the Bhatnagar-Gross-Krook approximation. The method
represents the six-dimensional BTE as a set of six one-dimensional problems,
which are solved with the alternating least-squares algorithm and the discrete
Fourier transform at $N$ collocation points. We use this method to predict the
equilibrium distribution (stead-state simulation) and a non-equilibrium
distribution returning to the equilibrium (transient simulation). Our numerical
experiments demonstrate $N \log N$ scaling. Unlike many BTE-specific numerical
techniques, the numerical tensor-decomposition method we propose is a general
technique that can be applied to other high-dimensional systems.
