Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 44, Issue 3, Pages B723-B745Publisher
SIAM PUBLICATIONS
DOI: 10.1137/20M1355884
Keywords
Key words; density functional theory; all-electron calculations; total energy minimization; orthogonalization-free; scalability
Categories
Funding
- Fonds de la Recherche Scientifique (FNRS)
- Fonds Wetenschappelijk Onderzoek-Vlaanderen [30468160]
- National Natural Science Foundation of China [12125108, 11971466, 11991021, 11922120, 11871489]
- FDCT of Macao SAR [0082/2020/A2]
- University of Macau [MYRG2020-00265-FST, MYRG2019-00154-FST]
- Guangdong-Hong Kong-Macao Joint Labora-tory for Data-Driven Fluid Mechanics and Engineering Applications [2020B1212030001]
- Academic Research Fund of the Ministry of Education of Singapore [R-146-000-291-114]
- Key Research Program of Frontier Sciences, Chinese Academy of Sciences [ZDBSLY-7022]
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All-electron calculations are crucial in density functional theory, and improving computational efficiency is a challenging task. In this paper, an orthogonalization-free algorithm framework is proposed to solve the nonlinear eigenvalue problem and the total energy minimization problem without invoking orthogonalization in each iteration, thereby enhancing computational efficiency and parallel scalability.
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 for-mulations, both the nonlinear eigenvalue problem and the 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 orthog-onality can be gradually achieved without invoking orthogonalization in each iteration. Moreover, this framework fully consists of BLAS operations and thus can be naturally parallelized. The global convergence of the proposed algorithm is established. We also present a preconditioning technique which can dramatically accelerate the convergence of the algorithm. The numerical experiments on all-electron calculations show the effectiveness and high scalability of the proposed algorithm.
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