메뉴 건너뛰기




Volumn 231, Issue 4, 2012, Pages 2140-2154

Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation

Author keywords

Adaptive local basis set; Discontinuous Galerkin; Eigenvalue problem; Electronic structure; Enrichment functions; Kohn Sham density functional theory

Indexed keywords

ATOMS; DENSITY FUNCTIONAL THEORY; EIGENVALUES AND EIGENFUNCTIONS; GALERKIN METHODS; HAMILTONIANS; NUMERICAL METHODS; QUANTUM CHEMISTRY;

EID: 84855163569     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.11.032     Document Type: Article
Times cited : (145)

References (54)
  • 1
    • 10644250257 scopus 로고
    • Inhomogeneous electron gas
    • Hohenberg P., Kohn W. Inhomogeneous electron gas. Phys. Rev. 1964, 136:B864-B871.
    • (1964) Phys. Rev. , vol.136
    • Hohenberg, P.1    Kohn, W.2
  • 2
    • 0042113153 scopus 로고
    • Self-consistent equations including exchange and correlation effects
    • Kohn W., Sham L. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140:A1133-A1138.
    • (1965) Phys. Rev. , vol.140
    • Kohn, W.1    Sham, L.2
  • 4
    • 33645426115 scopus 로고
    • Efficient pseudopotentials for plane-wave calculations
    • Troullier N., Martins J. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 1991, 43:1993-2006.
    • (1991) Phys. Rev. B , vol.43 , pp. 1993-2006
    • Troullier, N.1    Martins, J.2
  • 5
    • 3843133047 scopus 로고
    • Finite-difference-pseudopotential method: electronic structure calculations without a basis
    • Chelikowsky J., Troullier N., Saad Y. Finite-difference-pseudopotential method: electronic structure calculations without a basis. Phys. Rev. Lett. 1994, 72:1240-1243.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 1240-1243
    • Chelikowsky, J.1    Troullier, N.2    Saad, Y.3
  • 6
    • 1642346819 scopus 로고    scopus 로고
    • Real-space pseudopotential method for computing the electronic properties of periodic systems
    • Alemany M., Jain M., Kronik L., Chelikowsky J. Real-space pseudopotential method for computing the electronic properties of periodic systems. Phys. Rev. B 2004, 69:075101.
    • (2004) Phys. Rev. B , vol.69 , pp. 075101
    • Alemany, M.1    Jain, M.2    Kronik, L.3    Chelikowsky, J.4
  • 7
    • 33748870671 scopus 로고
    • Electronic-structure calculations based on the finite-element method
    • Tsuchida E., Tsukada M. Electronic-structure calculations based on the finite-element method. Phys. Rev. B 1995, 52:5573-5578.
    • (1995) Phys. Rev. B , vol.52 , pp. 5573-5578
    • Tsuchida, E.1    Tsukada, M.2
  • 8
    • 0000170529 scopus 로고    scopus 로고
    • Real-space local polynomial basis for solid-state electronic-structure calculations: a finite-element approach
    • Pask J., Klein B., Fong C., Sterne P. Real-space local polynomial basis for solid-state electronic-structure calculations: a finite-element approach. Phys. Rev. B 1999, 59:12352-12358.
    • (1999) Phys. Rev. B , vol.59 , pp. 12352-12358
    • Pask, J.1    Klein, B.2    Fong, C.3    Sterne, P.4
  • 9
    • 24144475862 scopus 로고    scopus 로고
    • Finite element methods in ab initio electronic structure calculations
    • Pask J., Sterne P. Finite element methods in ab initio electronic structure calculations. Modelling Simul. Mater. Sci. Eng. 2005, 13:R71.
    • (2005) Modelling Simul. Mater. Sci. Eng. , vol.13
    • Pask, J.1    Sterne, P.2
  • 11
    • 36749121581 scopus 로고
    • Efficient and accurate expansion methods for molecules in local density models
    • Delley B., Ellis D. Efficient and accurate expansion methods for molecules in local density models. J. Chem. Phys. 1982, 76:1949-1960.
    • (1982) J. Chem. Phys. , vol.76 , pp. 1949-1960
    • Delley, B.1    Ellis, D.2
  • 13
    • 0001174462 scopus 로고    scopus 로고
    • Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme
    • Koepernik K., Eschrig H. Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme. Phys. Rev. B 1999, 59:1743-1757.
    • (1999) Phys. Rev. B , vol.59 , pp. 1743-1757
    • Koepernik, K.1    Eschrig, H.2
  • 14
    • 0001653304 scopus 로고    scopus 로고
    • Transferable atomic-type orbital basis sets for solids
    • Kenny S., Horsfield A., Fujitani H. Transferable atomic-type orbital basis sets for solids. Phys. Rev. B 2000, 62:4899-4905.
    • (2000) Phys. Rev. B , vol.62 , pp. 4899-4905
    • Kenny, S.1    Horsfield, A.2    Fujitani, H.3
  • 15
  • 16
    • 0037495068 scopus 로고    scopus 로고
    • Variationally optimized atomic orbitals for large-scale electronic structures
    • Ozaki T. Variationally optimized atomic orbitals for large-scale electronic structures. Phys. Rev. B 2003, 67:155108.
    • (2003) Phys. Rev. B , vol.67 , pp. 155108
    • Ozaki, T.1
  • 18
    • 0000192466 scopus 로고
    • Wave functions in a periodic potential
    • Slater J.C. Wave functions in a periodic potential. Phys. Rev. 1937, 51:846-851.
    • (1937) Phys. Rev. , vol.51 , pp. 846-851
    • Slater, J.C.1
  • 19
    • 23244461569 scopus 로고
    • Linear methods in band theory
    • Andersen O.K. Linear methods in band theory. Phys. Rev. B 1975, 12:3060-3083.
    • (1975) Phys. Rev. B , vol.12 , pp. 3060-3083
    • Andersen, O.K.1
  • 20
    • 25744460922 scopus 로고
    • Projector augmented-wave method
    • Blöchl P.E. Projector augmented-wave method. Phys. Rev. B 1994, 50:17953-17979.
    • (1994) Phys. Rev. B , vol.50 , pp. 17953-17979
    • Blöchl, P.E.1
  • 21
    • 60949103522 scopus 로고    scopus 로고
    • Classical and enriched finite element formulations for Bloch-periodic boundary conditions
    • Sukumar N., Pask J. Classical and enriched finite element formulations for Bloch-periodic boundary conditions. Int. J. Numer. Methods Eng. 2009, 77:1121-1138.
    • (2009) Int. J. Numer. Methods Eng. , vol.77 , pp. 1121-1138
    • Sukumar, N.1    Pask, J.2
  • 22
    • 0001537143 scopus 로고
    • Nonconforming elements in the finite element method with penalty
    • BabuŠka I., Zlámal M. Nonconforming elements in the finite element method with penalty. SIAM J. Numer. Anal. 1973, 10:863-875.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 863-875
    • Babuška, I.1    Zlámal, M.2
  • 23
    • 0000802762 scopus 로고
    • An elliptic collocation-finite element method with interior penalties
    • Wheeler M. An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 1978, 15:152-161.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 152-161
    • Wheeler, M.1
  • 24
    • 0001163226 scopus 로고
    • An interior penalty finite element method with discontinuous elements
    • Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 1982, 19:742-760.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 742-760
    • Arnold, D.N.1
  • 26
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    • Cockburn B., Shu C.-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 2001, 16:173-261.
    • (2001) J. Sci. Comput. , vol.16 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 27
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • Arnold D.N., Brezzi F., Cockburn B., Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 2002, 39:1749.
    • (2002) SIAM J. Numer. Anal. , vol.39 , pp. 1749
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 28
    • 0038244441 scopus 로고    scopus 로고
    • A reduced-basis element method
    • Maday Y., Rønquist E. A reduced-basis element method. J. Sci. Comput. 2002, 17:447-459.
    • (2002) J. Sci. Comput. , vol.17 , pp. 447-459
    • Maday, Y.1    Rønquist, E.2
  • 29
    • 0037715324 scopus 로고    scopus 로고
    • Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations
    • Maday Y., Patera A., Turinici G. Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations. C.R. Acad. Sci. Paris. Ser. I 2002, 335:289-294.
    • (2002) C.R. Acad. Sci. Paris. Ser. I , vol.335 , pp. 289-294
    • Maday, Y.1    Patera, A.2    Turinici, G.3
  • 30
    • 39049136105 scopus 로고    scopus 로고
    • Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry
    • Amer. Math. Soc., Providence, RI, High-Dimensional Partial Differential Equations in Science and Engineering
    • Cancès E., Le Bris C., Maday Y., Nguyen N., Patera A., Pau G. Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry. CRM Proc. Lecture Notes 2007, vol. 41:15-47. Amer. Math. Soc., Providence, RI.
    • (2007) CRM Proc. Lecture Notes , vol.41 , pp. 15-47
    • Cancès, E.1    Le Bris, C.2    Maday, Y.3    Nguyen, N.4    Patera, A.5    Pau, G.6
  • 31
    • 77950893798 scopus 로고    scopus 로고
    • Certified reduced basis methods and output bounds for the harmonic Maxwell's equations
    • Chen Y., Hesthaven J., Maday Y., Rodri{dotless}́guez J. Certified reduced basis methods and output bounds for the harmonic Maxwell's equations. SIAM J. Sci. Comput. 2010, 32:970-996.
    • (2010) SIAM J. Sci. Comput. , vol.32 , pp. 970-996
    • Chen, Y.1    Hesthaven, J.2    Maday, Y.3    Rodrí guez, J.4
  • 32
    • 33748546239 scopus 로고    scopus 로고
    • Discontinuous Galerkin method based on non-polynomial approximation spaces
    • Yuan L., Shu C.-W. Discontinuous Galerkin method based on non-polynomial approximation spaces. J. Comput. Phys. 2006, 218:295-323.
    • (2006) J. Comput. Phys. , vol.218 , pp. 295-323
    • Yuan, L.1    Shu, C.-W.2
  • 33
    • 40749087210 scopus 로고    scopus 로고
    • Discontinuous Galerkin method for a class of elliptic multi-scale problems
    • Yuan L., Shu C.-W. Discontinuous Galerkin method for a class of elliptic multi-scale problems. Int. J. Numer. Methods Fluids 2007, 56:1017-1032.
    • (2007) Int. J. Numer. Methods Fluids , vol.56 , pp. 1017-1032
    • Yuan, L.1    Shu, C.-W.2
  • 34
    • 78649780397 scopus 로고    scopus 로고
    • The multiscale discontinuous Galerkin method for solving a class of second order elliptic problems with rough coefficients
    • Wang W., Guzmán J., Shu C.-W. The multiscale discontinuous Galerkin method for solving a class of second order elliptic problems with rough coefficients. Int. J. Numer. Anal. Model. 2011, 8:28-47.
    • (2011) Int. J. Numer. Anal. Model. , vol.8 , pp. 28-47
    • Wang, W.1    Guzmán, J.2    Shu, C.-W.3
  • 35
    • 0001161603 scopus 로고
    • Efficacious form for model pseudopotentials
    • Kleinman L., Bylander D. Efficacious form for model pseudopotentials. Phys. Rev. Lett. 1982, 48:1425-1428.
    • (1982) Phys. Rev. Lett. , vol.48 , pp. 1425-1428
    • Kleinman, L.1    Bylander, D.2
  • 36
    • 33744691386 scopus 로고
    • Ground state of the electron gas by a stochastic method
    • Ceperley D., Alder B. Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 1980, 45:566-569.
    • (1980) Phys. Rev. Lett. , vol.45 , pp. 566-569
    • Ceperley, D.1    Alder, B.2
  • 37
    • 26144450583 scopus 로고
    • Self-interaction correction to density-functional approximations for many-electron systems
    • Perdew J., Zunger A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 1981, 23:5048-5079.
    • (1981) Phys. Rev. B , vol.23 , pp. 5048-5079
    • Perdew, J.1    Zunger, A.2
  • 38
    • 11944256577 scopus 로고
    • Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients
    • Payne M., Teter M., Allan D., Arias T., Joannopoulos J. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 1992, 64:1045-1097.
    • (1992) Rev. Mod. Phys. , vol.64 , pp. 1045-1097
    • Payne, M.1    Teter, M.2    Allan, D.3    Arias, T.4    Joannopoulos, J.5
  • 39
    • 84945709150 scopus 로고
    • Iterative procedures for nonlinear integral equations
    • Anderson D. Iterative procedures for nonlinear integral equations. J. Assoc. Comput. Mach. 1965, 12:547-560.
    • (1965) J. Assoc. Comput. Mach. , vol.12 , pp. 547-560
    • Anderson, D.1
  • 40
    • 0000738606 scopus 로고
    • Modified Broyden's method for accelerating convergence in self-consistent calculations
    • Johnson D.D. Modified Broyden's method for accelerating convergence in self-consistent calculations. Phys. Rev. B 1988, 38:12807-12813.
    • (1988) Phys. Rev. B , vol.38 , pp. 12807-12813
    • Johnson, D.D.1
  • 41
    • 33947155839 scopus 로고    scopus 로고
    • Finite element approach for density functional theory calculations on locally-refined meshes
    • Fattebert J., Hornung R., Wissink A. Finite element approach for density functional theory calculations on locally-refined meshes. J. Comput. Phys. 2007, 223:759-773.
    • (2007) J. Comput. Phys. , vol.223 , pp. 759-773
    • Fattebert, J.1    Hornung, R.2    Wissink, A.3
  • 42
    • 0033248424 scopus 로고    scopus 로고
    • Multiresolution analysis of electronic structure: semicardinal and wavelet bases
    • Arias T. Multiresolution analysis of electronic structure: semicardinal and wavelet bases. Rev. Mod. Phys. 1999, 71:267.
    • (1999) Rev. Mod. Phys. , vol.71 , pp. 267
    • Arias, T.1
  • 44
    • 11044224123 scopus 로고    scopus 로고
    • Multiresolution quantum chemistry: basic theory and initial applications
    • Harrison R., Fann G., Yanai T., Gan Z., Beylkin G. Multiresolution quantum chemistry: basic theory and initial applications. J. Chem. Phys. 2004, 121:11587.
    • (2004) J. Chem. Phys. , vol.121 , pp. 11587
    • Harrison, R.1    Fann, G.2    Yanai, T.3    Gan, Z.4    Beylkin, G.5
  • 45
    • 0036223489 scopus 로고    scopus 로고
    • Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method
    • Knyazev A. Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method. SIAM J. Sci. Comput. 2001, 23:517-541.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 517-541
    • Knyazev, A.1
  • 46
    • 33645885675 scopus 로고
    • Solution of Schrödinger's equation for large systems
    • Teter M., Payne M., Allan D. Solution of Schrödinger's equation for large systems. Phys. Rev. B 1989, 40:12255-12263.
    • (1989) Phys. Rev. B , vol.40 , pp. 12255-12263
    • Teter, M.1    Payne, M.2    Allan, D.3
  • 47
    • 0000083717 scopus 로고    scopus 로고
    • Relativistic separable dual-space gaussian pseudopotentials from h to rn
    • Hartwigsen C., Gœdecker S., Hutter J. Relativistic separable dual-space gaussian pseudopotentials from h to rn. Phys. Rev. B 1998, 58:3641.
    • (1998) Phys. Rev. B , vol.58 , pp. 3641
    • Hartwigsen, C.1    Gœdecker, S.2    Hutter, J.3
  • 48
    • 20044374586 scopus 로고    scopus 로고
    • Real-space formulation of the electrostatic potential and total energy of solids
    • Pask J., Sterne P. Real-space formulation of the electrostatic potential and total energy of solids. Phys. Rev. B 2005, 71:113101.
    • (2005) Phys. Rev. B , vol.71 , pp. 113101
    • Pask, J.1    Sterne, P.2
  • 49
    • 71249126471 scopus 로고    scopus 로고
    • Pole-based approximation of the Fermi-Dirac function
    • Lin L., Lu J., Ying L., E W. Pole-based approximation of the Fermi-Dirac function. Chin. Ann. Math. Ser. B 2009, 30:729-742.
    • (2009) Chin. Ann. Math. Ser. B , vol.30 , pp. 729-742
    • Lin, L.1    Lu, J.2    Ying, L.3    E, W.4
  • 50
    • 70449396467 scopus 로고    scopus 로고
    • Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems
    • Lin L., Lu J., Ying L., Car R., E W. Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Commun. Math. Sci. 2009, 7:755-777.
    • (2009) Commun. Math. Sci. , vol.7 , pp. 755-777
    • Lin, L.1    Lu, J.2    Ying, L.3    Car, R.4    E, W.5
  • 51
    • 79960434376 scopus 로고    scopus 로고
    • A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations
    • Lin L., Yang C., Lu J., Ying L., E W. A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. SIAM J. Sci. Comput. 2011, 33:1329.
    • (2011) SIAM J. Sci. Comput. , vol.33 , pp. 1329
    • Lin, L.1    Yang, C.2    Lu, J.3    Ying, L.4    E, W.5
  • 52
    • 79952505499 scopus 로고    scopus 로고
    • SelInv - an algorithm for selected inversion of a sparse symmetric matrix
    • Lin L., Yang C., Meza J., Lu J., Ying L., E W. SelInv - an algorithm for selected inversion of a sparse symmetric matrix. ACM. Trans. Math. Software 2010, 37:40.
    • (2010) ACM. Trans. Math. Software , vol.37 , pp. 40
    • Lin, L.1    Yang, C.2    Meza, J.3    Lu, J.4    Ying, L.5    E, W.6
  • 53
    • 84931507903 scopus 로고
    • Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules I. Theory
    • Pulay P. Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules I. Theory. Mol. Phys. 1969, 17:197-204.
    • (1969) Mol. Phys. , vol.17 , pp. 197-204
    • Pulay, P.1
  • 54
    • 85190568251 scopus 로고    scopus 로고
    • Optimized local basis function for Kohn-Sham density functional theory
    • J. Comput. Phys. submitted for publication.
    • L. Lin, J. Lu, L. Ying, W. E, Optimized local basis function for Kohn-Sham density functional theory, J. Comput. Phys. (2011), submitted for publication.
    • (2011)
    • Lin, L.1    Lu, J.2    Ying, L.3    E, W.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.