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In this paper we construct numerical schemes to approximate linear transportequations with slab geometry by diffusion equations. We treat both the case ofpure diffusive scaling and the case where kinetic and diffusive scalingscoexist. The diffusion equations and their data are derived from asymptotic andlayer analysis which allows general scattering kernels and general data. Weapply the half-space solver in [20] to resolve the boundary layer equation andobtain the boundary data for the diffusion equation. The algorithms arevalidated by numerical experiments and also by error analysis for the purediffusive scaling case.

Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics