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