Numerics in BoRiS We develop a new 3D scrape-off layer (SOL) transport code for the modelling of a fusion device. For the description of the complex 3D geometry we use magnetic coordinates. With this coordinate transform we are able to use standard discretization methods. The different plasma regions have different magnetic coordinates. All regions can be hold in a single grid using our grid generation. par The Finite Volume Methods leads to large sparse linear systems of equations. Different iterative solvers (Krylov subspace projection methods including matrix-free variants) and preconditioners are compared with respect to their computational efficiency, grid size scaling and memory requirements. Different schemes for interpolation of fluxes and gradients on scattered 3D data for general convection-diffusion problems can be used.