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Volumn 50, Issue 7, 2011, Pages 2148-2156

Implementation and testing of Lanczos-based algorithms for Random-Phase Approximation eigenproblems

Author keywords

Bethe Salpeter equation; Iterative solvers; Tamm Dancoff approximation; Time dependent density functional theory

Indexed keywords

BETHE-SALPETER EQUATION; COMPUTATIONAL LOADS; EIGEN-PROBLEMS; HERMITIANS; ITERATIVE SOLVERS; LANCZOS; NON-HERMITIAN HAMILTONIANS; OPTICAL ABSORPTION; OPTICAL RESPONSE; RANDOM PHASE APPROXIMATIONS; TAMM-DANCOFF APPROXIMATION; TECHNICAL DETAILS; TIME-DEPENDENT DENSITY FUNCTIONAL THEORY;

EID: 79954423115     PISSN: 09270256     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.commatsci.2011.02.021     Document Type: Article
Times cited : (58)

References (38)
  • 5
    • 79954421421 scopus 로고    scopus 로고
    • note
    • RPA can be more efficient than the direct solution especially when one is interested only to a frequency range where the excitations are well separated.
  • 15
    • 34247324846 scopus 로고
    • In principle it is possible to choose a different energy range, not necessarily containing the lowest energy, using the modification proposed by G. Grosso, L. Martinelli and G. Pastori Parravini
    • Note that in the Lanczos approach the energy range includes always the lowest energies
    • Note that in the Lanczos approach the energy range includes always the lowest energies. In principle it is possible to choose a different energy range, not necessarily containing the lowest energy, using the modification proposed by G. Grosso, L. Martinelli and G. Pastori Parravini, Phys. Rev. B 51 (1995) 13033-13038.
    • (1995) Phys. Rev. B , vol.51 , pp. 13033-13038
  • 16
    • 0010610199 scopus 로고
    • H. Ehrenfest, F. Seitz, D. Turnbull (Eds.) Academic Press
    • R. Haydock, in: H. Ehrenfest, F. Seitz, D. Turnbull (Eds.), Solid State Phys. 35 (1980) 215, Academic Press.
    • (1980) Solid State Phys , vol.35 , pp. 215
    • Haydock, R.1
  • 18
    • 79954418986 scopus 로고    scopus 로고
    • note
    • In particular, at each iteration both the computational cost and the storage are increasing, since all the vectors in the basis are needed to determine the new one.
  • 19
    • 79954414582 scopus 로고    scopus 로고
    • note
    • In principle also the Hermitian algorithm can break down. In fact after many iterations, because of the numerical error, the vectors in the Lanczos basis may stop to be orthonormal.
  • 27
    • 79954420421 scopus 로고    scopus 로고
    • note
    • For real matrices, as in the case of TD-DFT for finite systems and local exchange-correlation functionals, the cost is reduced further, since one can construct before-hand the two matrix A = R + C and B = R - C, so that only a single matrix-vector multiplication is needed (giving another factor two). Moreover usually B reduces to a diagonal matrix, containing on the diagonal the energy differences of the particle-hole pairs. In this case the algorithm is equivalent to the one proposed by Casida, see Ref. [9].
  • 35
    • 79954420856 scopus 로고    scopus 로고
    • g.
    • g|


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.