Efficient block preconditioned eigensolvers for linear response timedependent density functional theory
Within this paper, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is selfadjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the Kinner product. Additionally, the solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing stateoftheartmore »
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Laboratory
 Publication Date:
 Report Number(s):
 PNNLSA114405
Journal ID: ISSN 00104655; PII: S0010465517302370
 Grant/Contract Number:
 AC0576RL01830; AC0205CH1123; AC0205CH11231; KC030106062653
 Type:
 Accepted Manuscript
 Journal Name:
 Computer Physics Communications
 Additional Journal Information:
 Journal Volume: 221; Journal ID: ISSN 00104655
 Publisher:
 Elsevier
 Research Org:
 Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21); Ministry of Education, Youth and Sports (Cambodia)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Time dependent density functional theory; Linear response eigenvalue problem; Preconditioned eigensolvers
 OSTI Identifier:
 1395271
Vecharynski, Eugene, Brabec, Jiri, Shao, Meiyue, Govind, Niranjan, and Yang, Chao. Efficient block preconditioned eigensolvers for linear response timedependent density functional theory. United States: N. p.,
Web. doi:10.1016/J.CPC.2017.07.017.
Vecharynski, Eugene, Brabec, Jiri, Shao, Meiyue, Govind, Niranjan, & Yang, Chao. Efficient block preconditioned eigensolvers for linear response timedependent density functional theory. United States. doi:10.1016/J.CPC.2017.07.017.
Vecharynski, Eugene, Brabec, Jiri, Shao, Meiyue, Govind, Niranjan, and Yang, Chao. 2017.
"Efficient block preconditioned eigensolvers for linear response timedependent density functional theory". United States.
doi:10.1016/J.CPC.2017.07.017. https://www.osti.gov/servlets/purl/1395271.
@article{osti_1395271,
title = {Efficient block preconditioned eigensolvers for linear response timedependent density functional theory},
author = {Vecharynski, Eugene and Brabec, Jiri and Shao, Meiyue and Govind, Niranjan and Yang, Chao},
abstractNote = {Within this paper, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is selfadjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the Kinner product. Additionally, the solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing stateoftheart Davidson type solvers by a factor of two in both solution time and storage.},
doi = {10.1016/J.CPC.2017.07.017},
journal = {Computer Physics Communications},
number = ,
volume = 221,
place = {United States},
year = {2017},
month = {8}
}