Once all the numerical ingredients for solving the Kohn-Sham equations in density functional theory are in place, a self-consistent solution is needed to obtain total energies, forces, and other properties at the Born-Oppenheimer surface. This talk discusses algorithms for density mixing and preconditioning to efficiently achieve self-consistency. The second part covers algorithms for (local) geometry optimization, based on the availability of total-energy gradients ("force") for the nuclear coordinates.
In the final part, the talk addresses developments to speed up individual Kohn-Sham density functional calculations using new hardware paradigms. In particular, the "changed thinking" for a GPU based implementation of an electronic structure code is discussed.