Scalable Parallel Numerical Methods and Software Tools for Material Design

Abstract

A new method of solution to the local spin density approximation to the electronic Schr\"{o}dinger equation is presented. The method is based on an efficient, parallel, adaptive multigrid eigenvalue solver. It is shown that adaptivity is both necessary and sufficient to accurately solve the eigenvalue problem near the singularities at the atomic centers. While preliminary, these results suggest that direct real space methods may provide a much needed method for efficiently computing the forces in complex materials.