  We present novel methods implemented within the non-equilibrium Green
function code (NEGF) transiesta based on density functional theory (DFT). Our
flexible, next-generation DFT-NEGF code handles devices with one or multiple
electrodes ($N_e\ge1$) with individual chemical potentials and electronic
temperatures. We describe its novel methods for electrostatic gating, contour
opti- mizations, and assertion of charge conservation, as well as the newly
implemented algorithms for optimized and scalable matrix inversion,
performance-critical pivoting, and hybrid parallellization. Additionally, a
generic NEGF post-processing code (tbtrans/phtrans) for electron and phonon
transport is presented with several novelties such as Hamiltonian
interpolations, $N_e\ge1$ electrode capability, bond-currents, generalized
interface for user-defined tight-binding transport, transmission projection
using eigenstates of a projected Hamiltonian, and fast inversion algorithms for
large-scale simulations easily exceeding $10^6$ atoms on workstation computers.
The new features of both codes are demonstrated and bench-marked for relevant
test systems.
