Introduction

As we have seen, the bottleneck in large Castep calculations is the explicit S-orthonormalisation of the eigenstates. This orthonormalisation involves the calculation and inversion of the band-overlap matrix, operations which scale as $N_pN_b^2$ and $N_b^3$ respectively, where $N_p$ is the number of plane-wave basis states and $N_b$ is the number of bands (eigenstates). Furthermore, when operating in band-parallel mode the former operation is also a communication bottleneck, as the individual eigenstates reside on different processing elements.

Clearly it is desirable to implement an optimisation scheme which will allow the approximate bands to be optimised without the need for an explicit S-orthonormalisation.