  We develop a computational framework, based on the Boltzmann transport
equation, with the ability to compute the thermal transport in nanostructured
materials of any geometry using as the only input the bulk thermal conductivity
accumulation function. The main advantage of our method is twofold. First,
while the scattering times and dispersion curves are unknown for most
materials, the phonon mean free path distribution can be directly obtained by
experiments. As a consequence, a wider range of materials can be simulated than
with a frequency-dependent approach. Second, when phonon dispersions are
available from first principles calculations, our approach allows one to
include easily the whole Brillouen zone in the calculations without
discretizing the phonon frequencies for all polarizations, reducing
considerably the computational effort. Furthermore, after deriving the
ballistic and diffusive limits of our model, we develop a multi-scale scheme
that couples phonon transport across different scales, enabling efficient
simulations of materials with wide phonon mean free path distributions. After
we validate our model against the frequency-dependent approach, we apply the
method to porous silicon membranes and find good agreement with experiments on
mesoscale pores. By enabling the investigation of thermal transport in
unexplored nanostructured materials, our method has potential to advance
high-efficiency thermoelectric devices.
