Finite element methods in ab initio electronic structure calculations

Modelling and Simulation in Materials Science and Engineering

Volumn 13, Issue 3, 2005, Pages

  Pask, J E ^a   Sterne, P A ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRONIC STRUCTURE; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; ITERATIVE METHODS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS; PROBABILITY DENSITY FUNCTION;

ITERATIVE SOLUTIONS; KOHN-SHAM EQUATIONS; PARALLEL IMPLEMENTATION; STRUCTURED MATRICES;

SOLIDS;

EID: 24144475862     PISSN: 09650393     EISSN: None     Source Type: Journal    
DOI: 10.1088/0965-0393/13/3/R01     Document Type: Review

References (87)

1. Hohenberg P and Kohn W 1964 Phys. Rev. 136 B864
2. Kohn W and Sham L J 1965 Phys. Rev. 140 A1133
3. For reviews see, e.g. Lang N D 1973 Solid State Phys. 28 255
4. Rajagopal A K 1979 Adv. Chem. Phys. 41 59
5. Kohn W and Vashishta P 1983 Theory of the Inhomogeneous Electron Gas ed S Lundqvist and N H March (New York: Plenum) p 79
6. Lang ND 1983 Theory of the Inhomogeneous Electron Gas ed S Lundqvist and N H March (New York: Plenum) p 309
7. Williams A R and von Barth V 1983 Theory of the Inhomogeneous Electron Gas ed S Lundqvist and N H March (New York: Plenum) p 189
8. Callaway J and March N H 1984 Solid State Phys. 38 135
9. Jones R O and Gunnarsson O 1989 Rev. Mod. Phys. 61 689
10. Zienkiewicz O C and Taylor R L 1988 The Finite Element Method 4th edn (New York: McGraw-Hill)
11. Strang G and Fix G J 1973 An Analysis of the Finite Element Method (Englewood Cliffs, NJ: Prentice-Hall)
12. Kardestuncer H et al (ed) 1987 Finite Element Handbook (New York: McGraw-Hill)
13. Singh D 1994 Plane Waves, Pseudopotentials and the LAPW Method (Dordrecht: Kluwer)
14. Pickett W E 1989 Comput. Phys. Rep. 9 115
15. White S R, Wilkins J W and Teter M P 1989 Phys. Rev. B 39 5819
16. Tsuchida E and Tsukada M 1995 Phys. Rev. B 52 5573
17. Skriver H L 1984 The LMTO Method (Berlin: Springer)
18. Yamakawa S and Hyodo S 2003 J. Alloys and Compounds 356-357 231
19. Vanderbilt D 1990 Phys. Rev. B 41 7892
20. Laasonen K, Car R, Lee C and Vanderbilt D 1991 Phys. Rev. B 43 6796
21. Rappe A M, Rabe K M, Kaxiras E and Joannopoulos J D 1990 Phys. Rev. B 41 1227
22. Lin J S, Qteish A, Payne M C and Heine V 1993 Phys. Rev. B 47 4174
23. Gygi F 1992 Europhys. Lett. 19 617
24. GygiF 1993 Phys. Rev. B 48 11692
25. Gygi F 1995 Phys. Rev. B 51 11190
26. Devenyi A, Cho K, Arias T A and Joannopoulos J D 1994 Phys. Rev. B 49 13373
27. Hamann D R 1995 Phys. Rev. B 51 7337
28. Hamann D R 1995 Phys. Rev. B 51 9508
29. Hamann D R 1996 Phys. Rev. B 54 1568
30. Goedecker S, Boulet M and Deutsch T 2003 Comput. Phys. Commun. 154 105
31. Canning A and Raczkowski D 2004 Bull. Am. Phys. 49 344
32. Skylaris C-K, Mostofi A A, Haynes P D, Diéguez O and Payne M C 2002 Phys. Rev. B 66 035119
33. Chelikowsky J R, Troullier N and Saad Y 1994 Phys. Rev. Lett. 72 1240
34. Chelikowsky J R, Troullier N, Wu K and Saad Y 1995 Phys. Rev. B 50 11355
35. Alemany M M G, Jain M, Kronik L and Chelikowsky J R 2004 Phys. Rev. B 69 075101
36. Seitsonen A P, Puska M J and Nieminen R M 1995 Phys. Rev. B 51 14057
37. Heiskanen M, Torsti T, Puska M J and Nieminen R M 2001 Phys. Rev. B 63 245106
38. Gygi F and Galli G 1995 Phys. Rev. B 52 R2229
39. Iyer K A, Merrick M P and Beck T L 1995 J. Chem. Phys. 103 227
40. Beck T L 2000 Rev. Mod. Phys. 72 1041
41. Hoshi T, Arai M and Fujiwara T 1995 Phys. Rev. B 52 R5459
42. Briggs E L, Sullivan D J and Bernholc J 1995 Phys. Rev. B 52 R5471
43. Briggs E L, Sullivan D J and Bernholc J 1996 Phys. Rev. B 54 14362
44. Modine N A, Zumbach G and Kaxiras E 1997 Phys Rev. B 55 10289
45. Waghmare U V, Kim H, Park I J, Modine N, Maragakis P and Kaxiras E 2001 Comput. Phys. Commun. 137 341
46. Fattebert J-L 1999 J. Comput. Phys. 149 75
47. Fattebert J-L and Nardelli M B 2003 Handbook of Numerical Analysis vol X (Amsterdam: Elsevier)
48. Foi- reviews see, e.g. Linderberg J 1987 Comput. Phys. Rep. 6 209
49. Neto J J S and Linderberg J 1991 Comput. Phys. Commun. 66 55
50. Ram-Mohan L R 2002 Finite Element and Boundary Element Applications in Quantum Mechanics (New York: Oxford University Press)
51. Hermansson B and Yevick D 1986 Phys. Rev. B 33 7241
52. Tsuchida E and Tsukada M 1996 Phys. Rev. B 54 7602
53. Tsuchida E and Tsukada M 1998 J. Phys. Soc. Japan 67 3844
54. Tsuchida E, Kanada Y and Tsukada M 1999 Chem. Phys. Lett. 311 236
55. Tsuchida E 2004 J. Chem. Phys. 121 4740
56. Pask J E, Klein B M, Fong C Y and Sterne P A 1999 Phys. Rev. B 59 12352
57. Pask J E, Klein B M, Sterne P A and Fong C Y 2001 Comput. Phys. Commun. 135 1
58. Pask J E and Sterne P A 2004 Handbook of Materials Modeling vol 1, ed R Carlow et al (Dordrecht: Kluwer) at press
59. Pask J E and Sterne P A 2005 Phys. Rev. B 71 113101
60. Jun S 2004 Int. J. Numer. Methods Eng. 59 1909
61. Payne M C, Teter M P, Allan D C, Arias T A and Joannopoulos J D 1992 Rev. Mod. Phys. 64 1045
62. Arias T A 1999 Rev. Mod. Phys. 71 267
63. Ashcroft N W and Mermin N D 1976 Solid State Physics (New York: Holt, Rinehart and Winston)
64. Cohen M L and Bergstresser T K 1966 Phys. Rev. 141 789
65. Madelung E 1918 Phys. Z. 19 524
66. Ewald P P 1921 Ann. Phys. 64253
67. Göttinger Nachr. Math.-Phys. Kl. II 3 55 1937
68. Wigner E and Seitz F 1933 Phys. Rev. 43 804
69. Wigner E and Seitz F 1934 Phys. Rev. 46 509
70. Fuchs K 1935 P roc. R. Soc. 151 585
71. Coldwell-Horsfall R A and Maradudin A A 1960 J. Math. Phys. 1 395
72. Ihm J, Zunger A and Cohen M L 1979 J. Phys. Condens. Matter 12 4409
73. Bachelet G B, Greenside H S, Baraff G A and Schlüter M 1981 Phys. Rev. B 24 4745
74. Baraff G A and Schlüter M 1983 Phys. Rev. B 28 2296
75. Baraff G A and Schlüter M 1984 Phys. Rev. B 30 1853
76. Ordejón P, Artacho E and Soler J M 1996 Phys. Rev. B 53 10441
77. Soler J M, Artacho E, Gale J D, García A, Junquera J, Ordejón P and Sánchez-Portal D 2002 J. Phys.: Condens. Matter 14 2745
78. Hartwigsen C, Goedecker S and Hutter J 1998 Phys. Rev. B 58 3641
79. Gonze X et al 2002 Comput. Mater. Sci. 25 478
80. The abinit code is a common project of the Université Catholique de Louvain, Corning Incorporated, and other contributors URL http://www.abinit.org
81. Perdew J P and Zunger A 1981 Phys. Rev. B 23
82. Chelikowsky J R and Louie S G 1984 Phys. Rev. B 29 3470
83. Sterne P A, Pask J E and Klein B M 1999 Appl Surf. Sci. 149 238
84. See, e.g. Puska M J and Nieminen R M 1994 Rev. Mod. Phys. 66 841
85. Becke A D 1988 Phys. Rev. A 38 3098
86. Lee C, Yang W and Parr R G 1988 Phys. Rev. B 37 785
87. Perdew J P, Burke K and Ernzerhof M 1996 Phys Rev. Lett. 77 3865