Detailed numerical methods for the three-dimensional quantum simulation of the multigate nanowire field effect transistors in the ballistic transport regime are presented in this work. The device has been modeled based on the effective mass theory and the non-equilibrium Green's function formalism, and its simulation consists of solutions of the three-dimensional Poisson's equation, two-dimensional Schrodinger equations on the cross-sectional planes, and one-dimensional transport equation. Details on numerical techniques for each of the simulation steps are described, with a special attention to the solution of the most CPU demanding two-dimensional Schrodinger equation. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.