Reduced-basis method for band structure calculations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 4, 2007, Pages

  Pau, George S H ^a,b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAND ENERGIES; BAND STRUCTURE CALCULATIONS; MANY QUERY LIMIT; REDUCED BASIS METHOD;

CRYSTALLINE MATERIALS; PROBLEM SOLVING; SILICON; SPECTRUM ANALYSIS;

BAND STRUCTURE;

EID: 35349022057     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.046704     Document Type: Article

References (42)

1. X. Wang, J. R. Yates, I. Souza, and D. Vanderbilt, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.195118 74, 195118 (2006).
2. S. Hamel, A. Williamson, H. Wilson, F. Gygi, G. Galli, E. Ratner, and D. Wack http://meetings.aps.org/link/BAPS.2007.MAR.L43.7.
3. H. Wilson, G. Galli, F. Gygi, S. Hamel, A. Williamson, E. Ratner, and D. Wack http://meetings.aps.org/link/BAPS.2007.MAR.J41.15.
4. I. Souza, N. Marzari, and D. Vanderbilt, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.035109 65, 035109 (2001).
5. N. Marzari and D. Vanderbilt, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.56.12847 56, 12847 (1997).
6. J. C. Slater and G. F. Koster, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.94.1498 94, 1498 (1954).
7. F. Gygi, J.-L. Fattebert, and E. Schwegler, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/S0010-4655(03)00315-1 155, 1 (2003).
8. B. O. Almroth, P. Stern, and F. A. Brogan, AIAA J. AIAJAH 0001-1452 16, 525 (1978).
9. A. K. Noor and J. M. Peters, AIAA J. AIAJAH 0001-1452 18, 455 (1980).
10. J. P. Fink and W. C. Rheinboldt, Z. Angew. Math. Mech. ZAMMAX 0044-2267 10.1002/zamm.19830630105 63, 21 (1983).
11. M. D. Gunzburger, Finite Element Methods for Viscous Incompressible Flows (Academic Press, New York, 1989).
12. K. Ito and S. S. Ravindran, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1998.5943 143, 403 (1998).
13. J. S. Peterson, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. SIJCD4 0196-5204 10, 777 (1989).
14. T. A. Porsching, Math. Comput. MCMPAF 0025-5718 10.2307/2008138 45, 487 (1985).
15. M. A. Grepl, N. C. Nguyen, K. Veroy, A. T. Patera, and G. R. Liu, in Towards Real-Time PDE-Constrained Optimization (SIAM, Philadelphia, 2007), pp. 197-216.
16. L. Machiels, Y. Maday, I. B. Oliveira, A. Patera, and D. Rovas, C. R. Acad. Sci., Ser. I: Math. 331, 153 (2000). 1064-5632
17. Y. Maday, A. T. Patera, and G. Turinici, C. R. Acad. Sci., Ser. I: Math. CASMEI 0764-4442. 335, 289 (2002).
18. C. Prud'homme, D. Rovas, K. Veroy, Y. Maday, A. Patera, and G. Turinici, J. Fluids Eng. JFEGA4 0098-2202 10.1115/1.1448332 124, 70 (2002).
19. N. C. Nguyen, K. Veroy, and A. T. Patera, in Handbook of Materials Modeling, edited by, S. Yip, (Springer, Berlin, 2005), pp. 1523-1558.
20. K. Veroy and A. T. Patera, Int. J. Numer. Methods Fluids IJNFDW 0271-2091 10.1002/fld.867 47, 773 (2005).
21. K. Veroy, C. Prud'homme, D. V. Rovas, and A. T. Patera, in Proceedings of the 16th AIAA Computational Fluid Dynamics Conference (AIAA, Orlando, 2003), paper 2003-3847.
22. M. Barrault, N. C. Nguyen, Y. Maday, and A. T. Patera, C. R. Acad. Sci., Ser. I: Math. 339, 667 (2004). 1064-5632
23. M. A. Grepl, Y. Maday, N. C. Nguyen, and A. T. Patera, Math. Modell. Numer. Anal. MMNAAB 0764-583X 10.1051/m2an:2007031 41, 575 (2007).
24. P. E. Blöchl, O. Jepsen, and O. K. Andersen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.16223 49, 16223 (1994).
25. O. Jepson and O. K. Anderson, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(71)90313-9 9, 1763 (1971).
26. G. Gilat and L. J. Raubenheimer, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.144.390 144, 390 (1966).
27. R. M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, U.K., 2004).
28. M. L. Cohen and T. K. Bergstresser, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.141.789 141, 789 (1966).
29. A. Baldereschi, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.7.5212 7, 5212 (1973).
30. A. D. Izaak, Math. Notes 55, 30 (1994). 0001-4346
31. S. N. Kudryavtsev, Math. Notes 77, 494 (2005). 0001-4346
32. A. Pinkus, Widths in Approximation Theory (Springer, Berlin, 1985).
33. Y. Maday, A. Patera, and G. Turinici, J. Sci. Comput. 17, 437 (2002). 0885-7474
34. Y. Maday, in International Congress of Mathematicians (Eur. Math. Soc., Zürich, 2006), Vol. III, pp. 1255-1270.
35. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer, New York, 1987).
36. G. S. H. Pau, Ph.D. thesis, Massachusetts Institute of Technology, 2007.
37. G. Strang and G. J. Fix, An Analysis of the Finite Element Method (Prentice-Hall, Englewood Cliffs, NJ, 1973).
38. Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia, 2000).
39. E. Isaacson and H. B. Keller, Computation of Eigenvalues and Eigenvectors, Analysis of Numerical Methods (Dover, New York, 1994).
40. B. N. Parlett, The Symmetric Eigenvalue Problem (SIAM, Philadelphia, 1998).
41. M. Ainsworth and J. T. Oden, A Posteriori Error Estimation in Finite Analysis (Wiley, New York, 2000).
42. A. K. Noor and I. Babška, Finite Elem. Anal. Design FEADEU 0168-874X 10.1016/0168-874X(87)90030-8 3, 1 (1987).