Matrix Structure Exploitation in Generalized Eigenproblems Arising in Density Functional Theory

Abstract

In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most well-known DFT implementations: FLAPW. Generating the Hamiltonian and overlap matrices and solving the associated generalized eigenproblems $Ax=\lambda Bx$ constitute the two most time-consuming fractions of each iteration. Two promising directions, implementing the new methodology, are presented that will ultimately improve the performance of the generalized eigensolver and save computational time.

To appear in the proceedings of 8th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2010)