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Volumn 20, Issue 12, 2010, Pages 2237-2265

Existence and convergence results for the galerkin approximation of an electronic density functional

Author keywords

Galerkin discretization; Nonlinear eigenvalue problem; Thomas Fermi type functionals

Indexed keywords

CONSTRAINED OPTIMIZATION PROBLEMS; CONVERGENCE RESULTS; ELECTRONIC DENSITY; EULER-LAGRANGE EQUATIONS; FINITE CLUSTERS; GALERKIN APPROXIMATIONS; GALERKIN DISCRETIZATION; LOCALIZED DEFECTS; NONLINEAR EIGENVALUE PROBLEM; ORBITAL-FREE DENSITY FUNCTIONAL THEORY; SADDLE POINT; THOMAS-FERMI;

EID: 78651245015     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021820251000491X     Document Type: Article
Times cited : (14)

References (36)
  • 9
    • 33744691386 scopus 로고
    • Ground state of the electron gas by a stochastic method
    • D. M. Ceperley and B. J. Alder, Ground state of the electron gas by a stochastic method, Phys. Rev. Lett. 45 (1980) 566-569.
    • (1980) Phys. Rev. Lett. , vol.45 , pp. 566-569
    • Ceperley, D.M.1    Alder, B.J.2
  • 11
    • 0012356898 scopus 로고
    • Finite element methods for nonlinear elliptic systems of second order
    • M. Dobrowolski and R. Rannacher, Finite element methods for nonlinear elliptic systems of second order, Math. Nachr. 94 (1980) 155-172.
    • (1980) Math. Nachr. , vol.94 , pp. 155-172
    • Dobrowolski, M.1    Rannacher, R.2
  • 12
    • 0003228130 scopus 로고    scopus 로고
    • Partial Differential Equations
    • Amer. Math. Soc.
    • L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19 (Amer. Math. Soc., 1998).
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 14
    • 35348939120 scopus 로고    scopus 로고
    • An e±cient real space method for orbital-free density-functional theory
    • C. J. García-Cervera, An e±cient real space method for orbital-free density-functional theory, Commun. Comput. Phys. 2 (2007) 334-357.
    • (2007) Commun. Comput. Phys. , vol.2 , pp. 334-357
    • García-Cervera, C.J.1
  • 15
    • 42949178584 scopus 로고    scopus 로고
    • A remark on \an e±cient real space method for orbital-free densityfunctional theory"
    • C. J. García-Cervera, A remark on \an e±cient real space method for orbital-free densityfunctional theory", Commun. Comput. Phys. 3 (2008) 968-972.
    • (2008) Commun Comput. Phys. , vol.3 , pp. 968-972
    • García-Cervera, C.J.1
  • 16
    • 39149107463 scopus 로고    scopus 로고
    • A sub-linear scaling algorithm for computing the electronic structure of materials
    • C. J. García-Cervera, J. Lu and W. E, A sub-linear scaling algorithm for computing the electronic structure of materials, Commun. Math. Sci. 5 (2007) 999-1026.
    • (2007) Commun. Math. Sci. , vol.5 , pp. 999-1026
    • García-Cervera, C.J.1    Lu, J.2
  • 17
    • 34047253234 scopus 로고    scopus 로고
    • Quasi- continuum orbital-free densityfunctional theory: A route to multi-million atom non-periodic DFT calculation
    • V. Gavini, K. Bhattacharya and M. Ortiz, Quasi-continuum orbital-free densityfunctional theory: A route to multi-million atom non-periodic DFT calculation, J. Mech. Phys. Solids 55 (2007) 697-718.
    • (2007) J. Mech. Phys. Solids , vol.55 , pp. 697-718
    • Gavini, V.1    Bhattacharya, K.2    Ortiz, M.3
  • 18
    • 34047254716 scopus 로고    scopus 로고
    • Non-periodic finite-element formulation of orbital-free density functional theory
    • V. Gavini, J. Knap, K. Bhattacharya and M. Ortiz, Non-periodic finite-element formulation of orbital-free density functional theory, J. Mech. Phys. Solids 55 (2007) 669-696.
    • (2007) J. Mech. Phys. Solids , vol.55 , pp. 669-696
    • Gavini, V.1    Knap, J.2    Bhattacharya, K.3    Ortiz, M.4
  • 19
    • 33646665354 scopus 로고
    • Density-functional theory of two-dimensional electron gas in a magnetic field
    • S. K. Ghosh and A. K. Dhara, Density-functional theory of two-dimensional electron gas in a magnetic field, Phys. Rev. A 40 (1989) 6103-6106.
    • (1989) Phys. Rev. A , vol.40 , pp. 6103-6106
    • Ghosh, S.K.1    Dhara, A.K.2
  • 21
    • 10644250257 scopus 로고
    • Inhomogeneous electron gas
    • P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964) B864-B871.
    • (1964) Phys. Rev. , vol.136
    • Hohenberg, P.1    Kohn, W.2
  • 22
    • 0033235339 scopus 로고    scopus 로고
    • Nobel lecture: Electronic structure of matterwave functions and density functionals
    • W. Kohn, Nobel Lecture: Electronic structure of matterwave functions and density functionals, Rev. Mod. Phys. 71 (1999) 1253-1266.
    • (1999) Rev. Mod. Phys. , vol.71 , pp. 1253-1266
    • Kohn, W.1
  • 23
    • 0042113153 scopus 로고
    • Self-consistent equations including exchange and correlation e® ects
    • W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation e® ects, Phys. Rev. 140 (1965) A1133-A1138.
    • (1965) Phys. Rev. , vol.140
    • Kohn, W.1    Sham, L.J.2
  • 25
    • 33847043281 scopus 로고
    • Thomas-Fermi and related theories of atoms and molecules
    • E. H. Lieb, Thomas-Fermi and related theories of atoms and molecules, Rev. Mod. Phys. 53 (1981) 603-641.
    • (1981) Rev. Mod. Phys. , vol.53 , pp. 603-641
    • Lieb, E.H.1
  • 26
    • 50349095129 scopus 로고    scopus 로고
    • An introduction to orbital-free density functional theory
    • Texts in Applied Mathematics , ed. S. Yip, Springer-Verlag, Sec. 1.8
    • L. Lignére and A. C. Carter, An introduction to orbital-free density functional theory, in Handbook of Materials Modeling, 2nd edn., Texts in Applied Mathematics, Vol. 15, ed. S. Yip (Springer-Verlag, 2005), Sec. 1.8.
    • (2005) Handbook of Materials Modeling, 2nd Edn. , vol.15
    • Lignére, L.1    Carter, A.C.2
  • 27
    • 0002958234 scopus 로고
    • First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems
    • H. Maurer and J. Zowe, First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems, Math. Programming 16 (1979) 98-110.
    • (1979) Math. Programming , vol.16 , pp. 98-110
    • Maurer, H.1    Zowe, J.2
  • 28
    • 55949117262 scopus 로고    scopus 로고
    • Quasicontinuum-like reduction of density functional theory calculations of nanostructures
    • D. Negrut, M. Anitescu, A. El-Azab and P. Zapol, Quasicontinuum-like reduction of density functional theory calculations of nanostructures, J. Nanosci. Nanotech. 8 (2008) 3729-3740.
    • (2008) J. Nanosci. Nanotech. , vol.8 , pp. 3729-3740
    • Negrut, D.1    Anitescu, M.2    El-Azab, A.3    Zapol, P.4
  • 29
    • 34249804310 scopus 로고    scopus 로고
    • Simulating nanoscale processes in solids using DFT and the quasicontinuum method (IMECE2005-81755)
    • D. Negrut, M. Anitescu, T. Munson and P. Zapol, Simulating nanoscale processes in solids using DFT and the quasicontinuum method (IMECE2005-81755), Proceedings of IMECE, 2005.
    • (2005) Proceedings of IMECE
    • Negrut, D.1    Anitescu, M.2    Munson, T.3    Zapol, P.4
  • 31
    • 26144450583 scopus 로고
    • Self-interaction correction to density-functional approximations for many-electron systems
    • J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23 (1981) 5048-5079.
    • (1981) Phys. Rev. B , vol.23 , pp. 5048-5079
    • Perdew, J.P.1    Zunger, A.2
  • 32
    • 84966217446 scopus 로고
    • An observation concerning Ritz- Galerkin methods with indefinite bilinear forms
    • A. H. Schatz, An observation concerning Ritz-Galerkin methods with indefinite bilinear forms, Math. Comp. 28 (1974) 959-962.
    • (1974) Math. Comp. , vol.28 , pp. 959-962
    • Schatz, A.H.1
  • 33
    • 0000658214 scopus 로고    scopus 로고
    • Orbital-free kinetic-energy functionals for the nearly free electron gas
    • Y. A. Wang, N. Govind and E. A. Carter, Orbital-free kinetic-energy functionals for the nearly free electron gas, Phys. Rev. B 58 (1998) 13465-13471.
    • (1998) Phys. Rev. B , vol.58 , pp. 13465-13471
    • Wang, Y.A.1    Govind, N.2    Carter, E.A.3
  • 34
    • 0001549358 scopus 로고    scopus 로고
    • Orbital-free kinetic-energy density functionals with a density-dependent kernel
    • Y. A. Wang, N. Govind and E. A. Carter, Orbital-free kinetic-energy density functionals with a density-dependent kernel, Phys. Rev. B 60 (1999) 16350-16358.
    • (1999) Phys. Rev. B , vol.60 , pp. 16350-16358
    • Wang, Y.A.1    Govind, N.2    Carter, E.A.3
  • 35
    • 0034625274 scopus 로고    scopus 로고
    • Linear-scaling parallel algorithms for the first principles treatment of metals
    • S. C. Watson and E. A. Carter, Linear-scaling parallel algorithms for the first principles treatment of metals, Comput. Phys. Commun. 128 (2000) 67-92.
    • (2000) Comput. Phys. Commun. , vol.128 , pp. 67-92
    • Watson, S.C.1    Carter, E.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.