메뉴 건너뛰기




Volumn 149, Issue 1, 1999, Pages 75-94

Finite Difference Schemes and Block Rayleigh Quotient Iteration for Electronic Structure Calculations on Composite Grids

Author keywords

Electronic structure calculations; Finite differences; Kohn Sham equations; Mesh refinement; Multigrid method; Rayleigh quotient iteration

Indexed keywords

CONTROL NONLINEARITIES; EIGENVALUES AND EIGENFUNCTIONS; ELECTRONIC STRUCTURE; FINITE DIFFERENCE METHOD; INVERSE PROBLEMS; ITERATIVE METHODS; MESH GENERATION; MOLECULES; NUMERICAL METHODS;

EID: 0002466739     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6138     Document Type: Article
Times cited : (37)

References (32)
  • 2
    • 3843133047 scopus 로고
    • Finite-difference-pseudopotential method: Electronic structure calculations without a basis
    • J. R. Chelikowsky, N. Trouiller, and Y. Saad, Finite-difference-pseudopotential method: Electronic structure calculations without a basis, Phys. Rev. Lett. 72(8), 1240 (1994).
    • (1994) Phys. Rev. Lett. , vol.72 , Issue.8 , pp. 1240
    • Chelikowsky, J.R.1    Trouiller, N.2    Saad, Y.3
  • 3
    • 0000328286 scopus 로고
    • Large scale electronic structure calculations with multigrid acceleration
    • E. L. Briggs, D. J. Sullivan, and J. Bernholc, Large scale electronic structure calculations with multigrid acceleration, Phys. Rev. B 52(8), 5471 (1995).
    • (1995) Phys. Rev. B , vol.52 , Issue.8 , pp. 5471
    • Briggs, E.L.1    Sullivan, D.J.2    Bernholc, J.3
  • 4
    • 0000054413 scopus 로고    scopus 로고
    • Real-space multigrid-based approach to large-scale electronic structure calculations
    • E. L. Briggs, D. J. Sullivan, and J. Bernholc, Real-space multigrid-based approach to large-scale electronic structure calculations, Phys. Rev. B 54(20), 14362 (1996).
    • (1996) Phys. Rev. B , vol.54 , Issue.20 , pp. 14362
    • Briggs, E.L.1    Sullivan, D.J.2    Bernholc, J.3
  • 5
    • 0347093108 scopus 로고    scopus 로고
    • An inverse iteration method using multigrid for quantum chemistry
    • J.-L. Fattebert, An inverse iteration method using multigrid for quantum chemistry, BIT 36(3), 509 (1996).
    • (1996) BIT , vol.36 , Issue.3 , pp. 509
    • Fattebert, J.-L.1
  • 7
    • 0000544586 scopus 로고
    • Real-space adaptive-coordinate electronic-structure calculations
    • F. Gygi and G. Galli, Real-space adaptive-coordinate electronic-structure calculations, Phys. Rev. B 52(4), 2229 (1995).
    • (1995) Phys. Rev. B , vol.52 , Issue.4 , pp. 2229
    • Gygi, F.1    Galli, G.2
  • 8
    • 0029292155 scopus 로고
    • Real space approach to electronic-structure calculations
    • E. Tsuchida and M. Tsukada, Real space approach to electronic-structure calculations, Solid State Com. 94(1), 5 (1995).
    • (1995) Solid State Com. , vol.94 , Issue.1 , pp. 5
    • Tsuchida, E.1    Tsukada, M.2
  • 9
  • 10
    • 0001686146 scopus 로고    scopus 로고
    • Adaptive-coordinate real-space electronic-structure calculations for atoms, molecules, and solids
    • N. A. Modine, G. Zumbach, and E. Kaxiras, Adaptive-coordinate real-space electronic-structure calculations for atoms, molecules, and solids, Phys. Rev. B 55(16), 10289 (1997).
    • (1997) Phys. Rev. B , vol.55 , Issue.16 , pp. 10289
    • Modine, N.A.1    Zumbach, G.2    Kaxiras, E.3
  • 12
    • 5344230920 scopus 로고
    • The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real symmetric matrices
    • E. R. Davidson, The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real symmetric matrices, J. Comput. Phys. 17, 87 (1975).
    • (1975) J. Comput. Phys. , vol.17 , pp. 87
    • Davidson, E.R.1
  • 14
    • 0030560293 scopus 로고    scopus 로고
    • A generalized Jacobi-Davidson iteration method for linear eigenvalue problem
    • G. L. G. Sleijpen and H. A. Van Der Vorst, A generalized Jacobi-Davidson iteration method for linear eigenvalue problem, SIAM Matrix Anal. Appl. 17(2), 401 (1996).
    • (1996) SIAM Matrix Anal. Appl. , vol.17 , Issue.2 , pp. 401
    • Sleijpen, G.L.G.1    Van Der Vorst, H.A.2
  • 15
    • 84966233568 scopus 로고
    • Multilevel adaptative solutions to boundary-value problems
    • A. Brandt, Multilevel adaptative solutions to boundary-value problems, Math. Comp. 31(138), 333 (1977).
    • (1977) Math. Comp. , vol.31 , Issue.138 , pp. 333
    • Brandt, A.1
  • 17
    • 33646638059 scopus 로고
    • Pseudopotential methods in condensed matter applications
    • W. E. Pickett, Pseudopotential methods in condensed matter applications, Comput. Phys. Rep. 9, 115 (1989).
    • (1989) Comput. Phys. Rep. , vol.9 , pp. 115
    • Pickett, W.E.1
  • 25
    • 85189851399 scopus 로고    scopus 로고
    • A block Rayleigh quotient iteration with local quadratic convergence
    • in press
    • J.-L. Fattebert, A block Rayleigh quotient iteration with local quadratic convergence, Elec. Trans. Num. Anal., in press.
    • Elec. Trans. Num. Anal.
    • Fattebert, J.-L.1
  • 26
    • 0000845335 scopus 로고
    • Local mesh refinement multilevel techniques
    • D. Bai and A. Brandt, Local mesh refinement multilevel techniques, SIAM J. Sci. Stat. Comput. 8(2), 109 (1987).
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , Issue.2 , pp. 109
    • Bai, D.1    Brandt, A.2
  • 27
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7(3), 856 (1986).
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , Issue.3 , pp. 856
    • Saad, Y.1    Schultz, M.H.2
  • 29
    • 85189846209 scopus 로고    scopus 로고
    • 3 plane waves, with periodic boundary conditions and adaptive coordinates (according to [32]) corresponding to a mesh refinement of a factor 2 in the regions where the functions vary rapidly]
    • 3 plane waves, with periodic boundary conditions and adaptive coordinates (according to [32]) corresponding to a mesh refinement of a factor 2 in the regions where the functions vary rapidly]
    • Gygi, F.1
  • 30
    • 0000625523 scopus 로고
    • Conjugate gradient minimization of the energy functional: A new method for electronic structure calculation
    • I. Stich, R. Car, M. Parrinello, and S. Baroni, Conjugate gradient minimization of the energy functional: A new method for electronic structure calculation. Phys. Rev. B 39(8), 4997 (1989).
    • (1989) Phys. Rev. B , vol.39 , Issue.8 , pp. 4997
    • Stich, I.1    Car, R.2    Parrinello, M.3    Baroni, S.4
  • 31
    • 0042927604 scopus 로고    scopus 로고
    • RQI (Rayleigh quotient iteration), an old recipe for solving modern large scale eigenvalue problems
    • J. Descloux, J.-L. Fattebert, and F. Gygi, RQI (Rayleigh quotient iteration), an old recipe for solving modern large scale eigenvalue problems, Comput. Phys. 12(1), 22 (1998).
    • (1998) Comput. Phys. , vol.12 , Issue.1 , pp. 22
    • Descloux, J.1    Fattebert, J.-L.2    Gygi, F.3
  • 32
    • 4244217973 scopus 로고
    • Electronic-structure calculations in adaptive coordinates
    • F. Gygi, Electronic-structure calculations in adaptive coordinates, Phys. Rev. B 48(16), 11692 (1993).
    • (1993) Phys. Rev. B , vol.48 , Issue.16 , pp. 11692
    • Gygi, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.