Conjugate-Gradient Based Electronic Structure Calculations on the Cray T3E and SGI PowerChallenge

Abstract

Electronic structure calculations based on Density Functional Theory (DFT) are an important branch of computational physics. We present a convergence analysis for the conjugate-gradient minimization of a Kohn-Sham energy functional, using a functional with implicit orthonormality constraints. We discuss the eects of preconditioning, and show with a numerical example that preconditioning makes the rate of convergence sensitive to the choice of the shift . We also present performance numbers for the 3d-FFT and matrix-matrix multiplies which are involved in the conjugate-gradient minimization within a pseudopotential/plane-wave approach. We compare the application performance of the SGI PowerChallenge as a typical symmetric multiprocessor to the one of the scalable Cray T3E at NERSC.