Abstract
In this paper, a preconditioning technique that is based on the finite differential approximation of the Hessian for non-linear conjugate gradient method is proposed and it was adapted to electronic structure calculation within finite element framework, i.e. the real space formula, which has the favorable nature for parallel computing. In the conventional electron calculations, namely the band structure methods, the conjugate gradient method has been also used with preconditioning. However, such preconditioning cannot be applied to the real space method. The efficiency of our new approach was explored in the computation of hydrogen electron structure. It has turned out that the proposed method was five times faster than no-preconditioning conjugate gradient method at maximum.
