Real-space local polynomial basis for solid-state electronic-structure calculations: a finite-element approach

Physical Review B - Condensed Matter and Materials Physics

Volumn 59, Issue 19, 1999, Pages 12352-12358

  Sterne, P A ^b   Klein, B M ^a   Fong, C Y ^a  

^a Lawrence Livermore National Laboratory ^*

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000170529     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.59.12352     Document Type: Article

References (57)

1. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964);
2. Phys. Rev.W. Kohn and L.J. Sham, 140, A1133 (1965).
3. See, e.g., W.E. Pickett, Comput. Phys. Rep. 9, 115 (1989) for a comprehensive review.
4. Matrix-vector multiplies—the central operations in iterative solution methods—scale at best as (Formula presented) as compared to N for sparse matrices, where N is the dimension of the matrices.
5. D. Vanderbilt, Phys. Rev. B 41, 7892 (1990);
6. Phys. Rev. BK. Laasonen, R. Car, C. Lee, and D. Vanderbilt, 43, 6796 (1991).
7. A.M. Rappe, K.M. Rabe, E. Kaxiras, and J.D. Joannopoulos, Phys. Rev. B 41, 1227 (1990).
8. J.S. Lin, A. Qteish, M.C. Payne, and V. Heine, Phys. Rev. B 47, 4174 (1993).
9. F. Gygi, Europhys. Lett. 19, 617 (1992);
10. F. GygiPhys. Rev. B 48, 11 692 (1993);
11. Phys. Rev. BF. Gygi51, 11 190 (1995).
12. A. Devenyi, K. Cho, T.A. Arias, and J.D. Joannopoulos, Phys. Rev. B 49, 13 373 (1994).
13. D.R. Hamann, Phys. Rev. B 51, 7337 (1995);
14. Phys. Rev. BD.R. Hamann51, 9508 (1995);
15. Phys. Rev. BD.R. Hamann56, 14 979 (1997).
16. J.R. Chelikowsky, N. Troullier, and Y. Saad, Phys. Rev. Lett. 72, 1240 (1994);
17. J.R. Chelikowsky, N. Troullier, K. Wu, and Y. Saad, Phys. Rev. B 50, 11 355 (1994);
18. Phys. Rev. BJ.R. Chelikowsky, 57, 3333 (1998).
19. E.L. Briggs, D.J. Sullivan, and J. Bernholc, Phys. Rev. B 52, R5471 (1995);
20. Phys. Rev. BE.L. BriggsD.J. SullivanJ. Bernholc54, 14 362 (1996);
21. J. Bernholc, E.L. Briggs, D.J. Sullivan, C.J. Brabec, M. Buongiorno Nardelli, K. Rapcewicz, C. Roland, and M. Wensell, Int. J. Quantum Chem. 65, 531 (1997).
22. G. Zumbach, N.A. Modine, and E. Kaxiras, Solid State Commun. 99, 57 (1996);
23. N.A. Modine, G. Zumbach, and E. Kaxiras, Phys. Rev. B 55, 10 289 (1997).
24. F. Gygi and G. Galli, Phys. Rev. B 52, R2229 (1995).
25. K.A. Iyer, M.P. Merrick, and T.L. Beck, J. Chem. Phys. 103, 227 (1995);
26. T.L. Beck, K.A. Iyer, and M.P. Merrick, Int. J. Quantum Chem. 61, 341 (1997);
27. Int. J. Quantum Chem.T.L. Beck, 65, 477 (1997).
28. T. Hoshi, M. Arai, and T. Fujiwara, Phys. Rev. B 52, R5459 (1995).
29. D.S. Burnett, Finite Element Analysis (Addison-Wesley, Reading, MA, 1987).
30. O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method, 4th ed. (McGraw-Hill, London, 1988).
31. K.-J. Bathe, Finite Element Procedures (Prentice Hall, Englewood Cliffs, NJ, 1996).
32. G. Strang and G.J. Fix, An Analysis of the Finite Element Method (Prentice-Hall, Englewood Cliffs, NJ, 1973).
33. K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Computational Differential Equations (Cambridge University Press, Cambridge, 1996).
34. B.D. Reddy, Introductory Functional Analysis (Springer-Verlag, New York, 1998).
35. For a review, see J. Linderberg, Comput. Phys. Rep. 6, 209 (1987);
36. J.J.S. Neto and J. Linderberg, Comput. Phys. Commun. 66, 55 (1991).
37. S.R. White, J.W. Wilkins, and M.P. Teter, Phys. Rev. B 39, 5819 (1989).
38. B. Hermansson and D. Yevick, Phys. Rev. B 33, 7241 (1986).
39. E. Tsuchida and M. Tsukada, Solid State Commun. 94, 5 (1995);
40. E. TsuchidaM. TsukadaPhys. Rev. B 52, 5573 (1995);
41. Phys. Rev. BE. TsuchidaM. Tsukada54, 7602 (1996).
42. J.E. Pask, B.M. Klein, and C.Y. Fong, Bull. Am. Phys. Soc. 43, 40 (1998).
43. See, e.g., Ref. 16.
44. R.L. Ferrari, Int. J. Numer. Modelling: Electronic Networks, Devices and Fields 6, 283 (1993).
45. K. Cho, T.A. Arias, J.D. Joannopoulos, and P.K. Lam, Phys. Rev. Lett. 71, 1808 (1993).
46. S. Wei and M.Y. Chou, Phys. Rev. Lett. 76, 2650 (1996).
47. C.J. Tymczak and X.Q. Wang, Phys. Rev. Lett. 78, 3654 (1997).
48. R.A. Lippert, T.A. Arias, and A. Edelman, J. Comput. Phys. 140, 278 (1998).
49. For details see, e.g., Ref. 21, Chap. 11;Ref. 16, Chaps. 5 and 13. The details of the additional step of piecing together across the domain boundary then follow straightforwardly from Sec. II.
50. A polynomial basis which is complete to order n spans the space of polynomials of order n.
51. A function is of class (Formula presented) if the function and its first n derivatives are continuous.
52. We assume that (Formula presented) is sufficiently well behaved to keep the integrals well defined. For details regarding the relevant function spaces, see, e.g., Refs. 19 and 21.
53. See e.g., Ref. 16, p. 426.
54. M.L. Cohen and T.K. Bergstresser, Phys. Rev. 141, 789 (1966).
55. P.A. Sterne, J.E. Pask, and B.M. Klein, Appl. Surf. Sci. (to be published).
56. See, e.g., Finite Element Handbook, edited by H. Kardestuncer et al. (McGraw-Hill, New York, 1987), p. 2.126.
57. This is among the most common methods of generating FE bases. For details, see, e.g., Ref. 16, Chaps. 8 and 13.