Improved generalized scattering matrix method:: Conduction through ballistic nanowires

We consider the generalized scattering matrix method for the solution of 3D scattering problems that can be well described by Helmholtz equation. A set of optimum strategies for the transversal basis selection, as well as for the mode matching algebra, are proposed; with them, a triple goal is achieved: to optimize the formulation, to simplify the implementation, and to increase computational speed. The proposed matrix truncation method provides quick convergence with one single parameter to be tuned. The matrix algebra used provides excellent stability vs the number of junctions as well as great computational speed. As illustrations and test, using the improved method, some aspects of the electronic transport through ballistic contacts are studied. Current vortex-rings in narrow-wide connections are predicted. A simple physical picture for the understanding of increasing conductance while pulling ideal monoatomic metal wires is proposed.