Abstract

All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the model formulations, both nonlinear eigenvalue problem and total energy minimization problem pursue orthogonal solutions. Most existing algorithms for solving these two models invoke orthogonalization process either explicitly or implicitly in each iteration. Their efficiency suffers from this process in view of its cubic complexity and low parallel scalability in terms of the number of electrons for large scale systems. To break through this bottleneck, we propose an orthogonalization-free algorithm framework based on the total energy minimization problem. It is shown that the desired orthogonality can be gradually achieved without invoking orthogonalization in each iteration. Moreover, this framework fully consists of Basic Linear Algebra Subprograms (BLAS) operations and thus can be naturally parallelized. The global convergence of the proposed algorithm is established. We also present a precondition technique which can dramatically accelerate the convergence of the algorithm. The numerical experiments on all-electron calculations show the efficiency and high scalability of the proposed algorithm.

About Dr. Kuang

Yang Kuang is a Research Fellow working with Prof. Zhenning Cai in the Department of Mathematics at National University of Singapore. He got his Ph.D. degree in Mathematics at University of Macau in 2019, under the supervision of Prof. Guanghui Hu. His research interests include adaptive finite element methods and efficient numerical algorithms for density functional theory. He is also interested in the complex Langevin methods in path integral computations.