  We have adapted R-matrix theory to calculate phonon scattering across systems
of molecular to mesoscopic scale. The key novelty of this work is that the only
required information about the scattering region are its normal modes, which
are evaluated only once for a system. Thus, R-matrix theory is a
computationally efficient and simple approach to calculate phonon scattering in
larger systems. To validate and to demonstrate the applicability of the theory,
we apply it to two systems: a one dimensional chain of atoms and a graphene
nanoribbon. In both cases, we discuss the effect of mass impurities on thermal
transport.
