  We study half-space linear kinetic equations with general boundary conditions
that consist of both given incoming data and various type of reflections,
extending our previous work [LLS14] on half-space equations with incoming
boundary conditions. As in [LLS14], the main technique is a damping
adding-removing procedure. We establish the well-posedness of linear (or
linearized) half-space equations with general boundary conditions and
quasi-optimality of the numerical scheme. The numerical method is validated by
examples including a two-species transport equation, a multi-frequency
transport equation, and the linearized BGK equation in 2D velocity space.
