Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration

TL;DR

This paper introduces a parallel Chebyshev-filtered subspace iteration method for solving the Kohn-Sham eigenvalue problem in density functional theory, significantly speeding up calculations and enabling previously infeasible complex simulations.

Contribution

The paper presents a novel parallel implementation of a Chebyshev-filtered subspace iteration method that reduces computational cost in DFT calculations compared to traditional eigensolvers.

Findings

Achieves self-consistency within a similar number of iterations as traditional methods

Provides significant speedup over standard diagonalization approaches

Enables complex DFT calculations previously considered infeasible

Abstract

Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first SCF iteration. The method may be viewed as an approach to solve the original nonlinear Kohn-Sham equation by a nonlinear subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problem. It reaches self-consistency within a similar number of SCF iterations as eigensolver-based approaches. However, replacing the standard diagonalization at each SCF iteration by a Chebyshev subspace filtering step results in a significant speedup over methods based on standard diagonalization. Here, we discuss an approach for implementing this method in multi-processor, parallel environment. Numerical results are presented to show that the method enables to perform a class of highly challenging DFT calculations that were not feasible before.