Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem
The Bethe–Salpeter eigenvalue problem is a dense structured eigenvalue problem arising from discretized Bethe–Salpeter equation in the context of computing exciton energies and states. A computational challenge is that at least half of the eigenvalues and the associated eigenvectors are desired in practice. In this paper, we establish the equivalence between Bethe–Salpeter eigenvalue problems and real Hamiltonian eigenvalue problems. Based on theoretical analysis, structure preserving algorithms for a class of Bethe–Salpeter eigenvalue problems are proposed. We also show that for this class of problems all eigenvalues obtained from the Tamm–Dancoff approximation are overestimated. In order to solve large scale problems of practical interest, we discuss parallel implementations of our algorithms targeting distributed memory systems. Finally, several numerical examples are presented to demonstrate the efficiency and accuracy of our algorithms.
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Linear Algebra and Its Applications
 Additional Journal Information:
 Journal Volume: 488; Journal ID: ISSN 00243795
 Research Org:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Contributing Orgs:
 Univ. of California, Berkeley, CA (United States)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Bethe–Salpeter equation; Tamm–Dancoff approximation; Hamiltonian eigenvalue problems; Structure preserving algorithms; Parallel algorithms
 OSTI Identifier:
 1378722
 Alternate Identifier(s):
 OSTI ID: 1359511
Shao, Meiyue, da Jornada, Felipe H., Yang, Chao, Deslippe, Jack, and Louie, Steven G.. Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem. United States: N. p.,
Web. doi:10.1016/j.laa.2015.09.036.
Shao, Meiyue, da Jornada, Felipe H., Yang, Chao, Deslippe, Jack, & Louie, Steven G.. Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem. United States. doi:10.1016/j.laa.2015.09.036.
Shao, Meiyue, da Jornada, Felipe H., Yang, Chao, Deslippe, Jack, and Louie, Steven G.. 2015.
"Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem". United States.
doi:10.1016/j.laa.2015.09.036. https://www.osti.gov/servlets/purl/1378722.
@article{osti_1378722,
title = {Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem},
author = {Shao, Meiyue and da Jornada, Felipe H. and Yang, Chao and Deslippe, Jack and Louie, Steven G.},
abstractNote = {The Bethe–Salpeter eigenvalue problem is a dense structured eigenvalue problem arising from discretized Bethe–Salpeter equation in the context of computing exciton energies and states. A computational challenge is that at least half of the eigenvalues and the associated eigenvectors are desired in practice. In this paper, we establish the equivalence between Bethe–Salpeter eigenvalue problems and real Hamiltonian eigenvalue problems. Based on theoretical analysis, structure preserving algorithms for a class of Bethe–Salpeter eigenvalue problems are proposed. We also show that for this class of problems all eigenvalues obtained from the Tamm–Dancoff approximation are overestimated. In order to solve large scale problems of practical interest, we discuss parallel implementations of our algorithms targeting distributed memory systems. Finally, several numerical examples are presented to demonstrate the efficiency and accuracy of our algorithms.},
doi = {10.1016/j.laa.2015.09.036},
journal = {Linear Algebra and Its Applications},
number = ,
volume = 488,
place = {United States},
year = {2015},
month = {10}
}