  We consider the numerical approximation of boundary conditions in radiative
transfer problems by a perfectly matched layer approach. The main idea is to
extend the computational domain by an absorbing layer and to use an appropriate
reflection boundary condition at the boundary of the extended domain. A careful
analysis shows that the consistency error introduced by this approach can be
made arbitrarily small by increasing the size of the extension domain or the
magnitude of the artificial absorption in the surrounding layer. A particular
choice of the reflection boundary condition allows us to circumvent the
half-space integrals that arise in the variational treatment of the original
vacuum boundary conditions and which destroy the sparse coupling observed in
numerical approximation schemes based on truncated spherical harmonics
expansions. A combination of the perfectly matched layer approach with a mixed
variational formulation and a PN-finite element approximation leads to
discretization schemes with optimal sparsity pattern and provable quasi-optimal
convergence properties. As demonstrated in numerical tests these methods are
accurate and very efficient for radiative transfer in the scattering regime.
