An orthogonalization-free implementation of the LOBPCG method in solving Kohn-Sham equation

TL;DR

This paper introduces an orthogonalization-free LOBPCG method for solving the Kohn-Sham equation, significantly reducing computational time and improving efficiency in SCF iterations through parallelization and preconditioning.

Contribution

It presents a novel orthogonalization-free framework for LOBPCG, with parallelized R-R procedure and effective preconditioning, enhancing computational efficiency in electronic structure calculations.

Findings

Significant reduction in computational time observed.

Effective preconditioning accelerates convergence.

Parallel implementation improves scalability.

Abstract

In the classic implementation of the LOBPCG method, orthogonalization and the R-R (Rayleigh-Ritz) procedure cost nonignorable CPU time. Especially this consumption could be very expensive to deal with situations with large block sizes. In this paper, we propose an orthogonalization-free framework of implementing the LOBPCG method for SCF (self-consistent field) iterations in solving the Kohn-Sham equation. In this framework, orthogonalization is avoided in calculations, which can decrease the computational complexity. And the R-R procedure is implemented parallelly through OpenMP, which can further reduce computational time. During numerical experiments, an effective preconditioning strategy is designed, which can accelerate the LOBPCG method remarkably. Consequently, the efficiency of the LOBPCG method can be significantly improved. Based on this, the SCF iteration can solve the Kohn-Sham equation efficiently. A series of numerical experiments are inducted to demonstrate the effectiveness of our implementation, in which significant improvements in computational time can be observed.