This chapter introduces the Korringa-Kohn-Rostoker (KKR) method and describes its features, which allows for addressing challenging problems in materials science. One of the most promising approaches for realizing exascale computers is the use of computer devices, which are operated at relatively low clock frequency but are capable of performing an extremely larger number of floating-point operations each clock cycle. Access to the KKR nano-repository is currently available in the context of scientific collaboration with the Institute for Advanced Simulation because the code has not yet been released under a public license. The simple properties of the most performance critical kernel, namely the operator solver based on the TFMQR algorithm, make this application suitable for unconventional architectures. The combination of a throughput-optimized compute accelerator with a general-purpose central processing unit makes the choice of clock speeds of both chips an important task.