Design structures of semiconductor circuits have shrunk to the lengthscale of a few nanometers. Despite that, systems so far have been too large to predict the electronic structure of realistic nano devices with an atom model description as accurate as density functional theory (DFT). DFT eigenvalue problems leads to an unaffordable cubic scaling behaviour of the total workload, no matter how smart the diagonalization algorithm is. Density matrix-based DFT algorithms allow for linear-scaling and hence millions of atoms, however, they require a band-gapped system, i.e. conducting leads are problematic. Green function based DFT allows for both, metallic systems and linear-scaling due to truncation. In this work, Green function DFT is expanded to real-space grids to be able to achieve an accuracy comparable to that of a plane-wave basis. The core of this algorithm is a GPU-accelerated implicit Hamiltonian operator that is applied repeatedly to find the grid-resolved Green function by using an iterative residual minimization technique. Key to high performance are reduced GPU-memory bandwidth requirements of the implicit Hamiltonian.An important ingredient are factorizable projector functions for the pseudopotential that are computed on the fly. We show details of the CUDA-C++ implementation and first performance numbers.