Finite element approach for density functional theory calculations on locally-refined meshes

We present a quadratic finite element approach to discretize the Kohn–Sham equations on structured non-uniform meshes. A multigrid FAC preconditioner is proposed to iteratively solve the equations by an accelerated steepest descent scheme. The method was implemented using SAMRAI, a parallel software infrastructure for general AMR applications. Examples of applications to small nanoclusters calculations are presented.