期刊
COMPUTER PHYSICS COMMUNICATIONS
卷 183, 期 3, 页码 497-505出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2011.11.005
关键词
Spectrum slicing; Hermitian eigenproblem; Kohn-Sham equation; Sparse parallel eigensolver; Polynomial filtering
资金
- National Science Foundation [DMR-0941645, OCI-1047997]
- Welch Foundation [F-1708]
- Office of Science of the U.S. Department of Energy [DE-AC02-05CH11231, DE-AC05-00OR22725]
- National Science Foundation through TeraGrid at the Texas Advanced Computing Center (TACC) [TG-DMR090026]
- Direct For Computer & Info Scie & Enginr
- Office of Advanced Cyberinfrastructure (OAC) [1047997] Funding Source: National Science Foundation
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [0941645] Funding Source: National Science Foundation
- Office of Advanced Cyberinfrastructure (OAC)
- Direct For Computer & Info Scie & Enginr [1047961] Funding Source: National Science Foundation
Solving the Kohn-Sham equation, which arises in density functional theory, is a standard procedure to determine the electronic structure of atoms, molecules, and condensed matter systems. The solution of this nonlinear eigenproblem is used to predict the spatial and energetic distribution of electronic states. However, obtaining a solution for large systems is computationally intensive because the problem scales super-linearly with the number of atoms. Here we demonstrate a divide and conquer method that partitions the necessary eigenvalue spectrum into slices and computes each partial spectrum on an independent group of processors in parallel. We focus on the elements of the spectrum slicing method that are essential to its correctness and robustness such as the choice of filter polynomial, the stopping criterion for a vector iteration, and the detection of duplicate eigenpairs computed in adjacent spectral slices. Some of the more prominent aspects of developing an optimized implementation are discussed. (C) 2011 Elsevier B.V. All rights reserved.
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