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

Bernd Pfrommer - Steven G. Louie - Horst Simon

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 effects 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.

• Introduction
• Unconstrained Energy Functional
• Convergence Analysis
• A numerical example
• Parallel Performance on the Cray T3E and SGI PowerChallenge
• References