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Title: Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem

Journal Article · · Linear Algebra and Its Applications
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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.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES)
Contributing Organization:
Univ. of California, Berkeley, CA (United States)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1580685
Alternate ID(s):
OSTI ID: 1359511; OSTI ID: 1378722
Journal Information:
Linear Algebra and Its Applications, Journal Name: Linear Algebra and Its Applications Vol. 488 Journal Issue: C; ISSN 0024-3795
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 31 works
Citation information provided by
Web of Science

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Related Subjects

97 MATHEMATICS AND COMPUTING
Bethe–Salpeter equation
Tamm–Dancoff approximation
Hamiltonian eigenvalue problems
Structure preserving algorithms
Parallel algorithms