  The capabilities of CP2K, a density-functional theory package and OMEN, a
nano-device simulator, are combined to study transport phenomena from
first-principles in unprecedentedly large nanostructures. Based on the
Hamiltonian and overlap matrices generated by CP2K for a given system, OMEN
solves the Schroedinger equation with open boundary conditions (OBCs) for all
possible electron momenta and energies. To accelerate this core operation a
robust algorithm called SplitSolve has been developed. It allows to
simultaneously treat the OBCs on CPUs and the Schroedinger equation on GPUs,
taking advantage of hybrid nodes. Our key achievements on the Cray-XK7 Titan
are (i) a reduction in time-to-solution by more than one order of magnitude as
compared to standard methods, enabling the simulation of structures with more
than 50000 atoms, (ii) a parallel efficiency of 97% when scaling from 756 up to
18564 nodes, and (iii) a sustained performance of 15 DP-PFlop/s.
