Abstract
In this paper, we consider spatially homogeneous linear kinetic models arising from semiconductor device simulations and investigate how various deterministic numerical methods approximate their scattering operators. In particular, methods including first and second order discontinuous Galerkin methods, a first order collocation method, a Fourier-collocation spectral method, and a Nyström method are examined when they are applied to one-dimensional models with singular or continuous scattering kernels. Mathematical properties are discussed for the corresponding discrete scattering operators. We also present numerical experiments to demonstrate the performance of these methods. Understanding how the scattering operators are approximated can provide insights into designing efficient algorithms for simulating kinetic models and for the implicit discretizations of the problems in the presence of multiple scales.