Multiresolution analysis of electronic structure: Semicardinal and wavelet bases

Reviews of Modern Physics

Volumn 71, Issue 1, 1999, Pages 267-311

  Arias, T A ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033248424     PISSN: 00346861     EISSN: None     Source Type: Journal    
DOI: 10.1103/revmodphys.71.267     Document Type: Review

References (88)

1. Adler, D., H. Fritzsche, and S. Ovshinsky, Eds., 1985, Physics of Disordered Materials (Plenum, New York).
2. Ainsworth, M., J. Levesley, M. Marletta, W. Light, and E. Nu, Eds., 1997, Wavelets, Multilevel Methods and Ellipic Pde's, Numerical Mathematics and Scientific Computation (Oxford University Press, Oxford).
3. Akay, M., Eds., 1997, Time Frequency and Wavelets in Biomedical Signal Processing, IEEE Press Series in Biomedical Engineering (IEEE Press, Piscataway).
4. Aldroubi, A., and M. Unser, 1993, Numer. Funct. Anal. Optim. 14, 417.
5. Andersen, O., 1975, Phys. Rev. B 12, 3060.
6. Arias, T., 1995, Annual March Meeting of the Americal Physical Society, San Jose, California.
7. Arias, T., K. Cho, P. Lam, and M. Teter, 1995, in Proceedings of the '94 Mardi Gras Conference: Toward Teraflop Computing and New Grand Challenge Applications, edited by R. K. Kalia, and P. Vashishta (Nova Science Publishers, Commack New York), p. 23.
8. Arias, T. A., M. C. Payne, and J. D. Joannopoulos, 1992, Phys. Rev. Lett. 71, 1077-1080.
9. Beck, T. L., M. P. Merrick, and K. A. Iyer, 1995, in Proceedings of the 1995 Simulation Multiconference: Grand Challenges in Computer Simulation, edited by A. Tentner (SCS, San Diego), p. 141.
10. Bertoluzza, S., and G. Naldi, 1996, Appl. Comput. Harmon. Anal. 3, 1.
11. Beylkin, G., R. Coifman, and V. Rokhlin, 1991, Commun. Pure Appl. Math. 44, 141.
12. Beylkin G., and J. M. Keiser, 1995, PAM Report.
13. Beylkin, G., and J. M. Keiser, 1997, J. Comput. Phys. 132, 233.
14. Beylkin, G., and N. Saito, 1992, expanded abstract in Proceedings ICASSP-92, San Francisco, Vol. 4, p. 381.
15. Braess, D., 1997, Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics (Cambridge University Press, Cambridge, U.K.).
16. Briggs, E., D. Sullivan, and J. Bernholc, 1996, Phys. Rev. B 54, 14 362.
17. Chandrupatla, T., and A. Belegundu, 1997, Introduction to Finite Elements in Engineering (Prentice Hall, Upper Saddle River, NJ).
18. Cho, K., T. Arias, J. Joannopoulos, and P. K. Lam, 1993, Phys. Rev. Lett. 71, 1808.
19. Chui, C., 1992, An Introduction to Wavelets (Academic Press, Boston).
20. Chui, C., and X. Shi, 1992, in Wavelets and multiscale interpolation, edited by T. Lyche, and L. Schumaker (Academic Press, Boston), p. 11.
21. Chung, T., 1992, Finite Elements in Fluids, Series in Computational and Physical Processes in Mechanics and Thermal Sciences (Wiley, Chichester, NY).
22. Cohen, A., and R. Danchin, 1997, preprint.
23. Cohen, M., 1984, Phys. Rep. 110, 293.
24. Csányi, G., S. Ismail-Beigi, and T. Arias, 1998, Phys. Rev. Lett. 80, 3984.
25. Dahmen, W., A. J. Kurdila, and P. Oswald, Eds., 1997, Multiscale Wavelet Methods for Partial Differential Equations, Vol. 6 of Wavelet Analysis and Its Applications (Academic Press, San Diego).
26. D'Attellis, C. E., and E. M. Fernandez-Berdaguer, Eds., 1997, Wavelet Theory and Harmonic Analysis in Applied Sciences, Applied and Numerical Harmonic Analysis (Birkhauser, Boston).
27. Daubechies, I., 1992, Ten Lectures on Wavelets, CBMS/NSF Series in Applied Math. No. 61 (SIAM, Philadelphia).
28. Deslauriers, G., and S. Dubuc, 1989, Constr. Approx. 5(1), 49 (ISSN 0176-4276, published by Springer-Verlag, NY).
29. Devenyi, A., T. A. K. Cho, and J. Joannopoulos, 1994, Phys. Rev. B 49, 13 373.
30. Donoho, D. L., 1992, preprint, Department of Statistics, Stanford Unversity.
31. Feller, D., and E. R. Davidson, 1990, Basis Sets for Ab Initio Molecular Orbital Calculations and Intermolecular Interactions, Vol. 1 of Reviews in Computational Chemistry (VCH, New York).
32. Frohlich, J., and K. Schneider, 1994, Eur. J. Mech. B/Fluids 13, 439.
33. Frohlich, J., and K. Schneider, 1997, J. Comput. Phys. 130, 174.
34. Goedecker, S., 1998, Wavelets and Their Application for the Solution of Partial Differential Equations in Physics (Presses Polytechniques et Universitaires Romandes, Lausanne, Switzerland).
35. Goedecker, S., and O. Ivanov, 1998, Solid State Commun. 105, 665.
36. Gopinath, R. A., H. Guo, C. S. Burrus, and L. S. Burrus, 1997, Introduction to Wavelets and Wavelet Transforms: A Primer (Prentice Hall, Upper Saddle River, NJ).
37. Greengard, L., and V. Rokhlin, 1989, Chem. Scr. 29A, 139.
38. Gygi, F., 1993, Europhys. Lett. 19, 617.
39. Gygi, F., 1995, Phys. Rev. B 51, 11190.
40. Gygi, F., and G. Galli, 1995, Phys. Rev. B 52, R2229.
41. Hamann, D., 1995, Phys. Rev. B 51, 7377.
42. Hamann, D., 1996a, Phys. Rev. B 54, 1568.
43. Hamann, D., 1996b, Phys. Rev. Lett. 76, 660.
44. Hamann, D., 1997, Phys. Rev. B 56, 14 979.
45. Hernandez, E., and G. L. Weiss, 1996, A First Course on Wavelets, Studies in Advanced Mathematics (CRS Press, Boca Raton).
46. Hohenberg, P., and W. Kohn, 1964, Phys. Rev. 136, B864.
47. Ismail-Beigi, S., and T. Arias, 1998, Phys. Rev. B 57, 11 923.
48. Kaiser, G., 1994, A Friendly Guide to Wavelets (Birkhauser, Boston).
49. Kohn, W., and L. J. Sham, 1965, Phys. Rev. 140, A1133.
50. Lemarié, P., 1991, Université Paris Sud, Technical Report 91-13.
51. Lewis, R. M., 1994, J. Approx. Theory 76, 177.
52. Liandrat, J., V. Pierrier, and P. Tchamitchian, 1989, Technical Report CPT-89/P.2320, Center of Theoretical Physics, Marseille, France.
53. Liandrat, J., and P. Tchamitchian, December 1990, Technical Report 90-83, NASA ICASE, report.
54. Lippert, R., 1998, Ph.D. thesis, M.I.T.
55. Lippert, R., T. Arias, and A. Edelman, 1998, J. Comput. Phys. 140, 278.
56. Mallat, S., 1989, Trans. Am. Math. Soc. 315, 69.
57. Meyer, Y., 1986, lectures given at the University of Torino, Italy.
58. Meyer, Y., 1990, Ondeletts et Opérateurs (Herman, Paris).
59. Meyer, Y., R. Coiffman, and R. Coifman, 1997, Wavelets: Calderon-Zygmund and Multilinear Operators, Vol. 48 of Cambridge Studies in Advanced Mathematics (Cambridge University Press, Cambridge, U.K.).
60. Monkhorst, H., and J. Pack, 1976, Phys. Rev. B 13, 5188.
61. Motard, R. L., and B. Joseph, Eds., 1994, Wavelet Applications in Chemical Engineering (Kluwer Academic Publishers, Boston).
62. Nakano, A., and T. Campbell, 1997, Parallel Comput. 23, 1461.
63. Payne, M., M. Teter, D. Allan, T. Arias, and J. Joannopoulos, 1992, Rev. Mod. Phys. 64, 1045.
64. Perdew, J., and A. Zunger, 1981, Phys. Rep. 23, 5048.
65. Pickett, W., 1989, Comput. Phys. Rep. Lett. 9, 115.
66. Pittner, S., J. Schneid, and C. W. Ueberhuber, 1993, The Wavelet Literature Survey (Institute for Applied and Numerical Mathematics, Vienna).
67. Rank, E., 1993, in Adaptive Finite and Boundary Element Methods, edited by C. Brebbia, and M. Aliabaldi (Computational Mechanics Publications, Southampton).
68. Rieder, A., R. O. Wells, Jr., and X. Zhou, 1994, Appl. Comput. Harmon. Anal. 1, 355.
69. Saito, N., and G. Beylkin, 1993, IEEE Trans. Signal Process. 41, 3584.
70. Singh, D., 1994, Planewaves, Pseudopotentials and the LAPW Method (Kluwer Academic Publishers, Netherlands).
71. G. Strang, and T. Nguyen, 1996, Wavelets and Filter Banks (Wellesley-Cambridge Press, Wellesley).
72. Suter, B. W., 1998, Multirate and Wavelet Signal Processing, Vol. 8 of Wavelet Analysis and Its Applications (Academic Press, San Diego).
73. Sweldens, W., 1996, Appl. Comput. Harm. Anal. 3, 186.
74. Teter, M., 1993, private communication.
75. Tsuchida, E., and M. Tsukada, 1995a, Phys. Rev. B 52, 5573.
76. Tsuchida, E., and M. Tsukada, 1995b, Solid State Commun. 94, 5.
77. Tsuchida, E., and M. Tsukada, 1996, Phys. Rev. B 54, 7602.
78. Tymczak, C., and X.-Q. Wang, 1997, Phys. Rev. Lett. 78, 3654.
79. Unser, M., 1993, in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE Press, Piscataway), Vol. 5.
80. Vasilyev, O., D. Yuen, and S. Paolucci, 1997, Comput. Phys. 11, 429.
81. Wei, S., and M. Chou, 1996, Phys. Rev. Lett. 76, 2650.
82. Wesseling, P., 1992, An Introduction to Multigrid Methods (Wiley, Chichester, N.Y.).
83. White, S., J. Wilkins, and M. Teter, 1989, Phys. Rev. B 39, 5819.
84. Whiteman, J., Eds., 1997, The Mathematics of Finite Elements and Applications: Highlights 1996 (John Wiley & Sons, New York).
85. Wimmer, E., H. Krakauer, M. Weinert, and A. Freeman, 1981, Phys. Rev. B 24, 864.
86. Yesilleten, D., 1997, S.B. thesis, Department of Physics M.I.T.
87. Yesilleten, D., and T. Arias, 1998, xxx.lanl.gov e-print archive physics/9806034.
88. Zumback, G., N. Modine, and E. Kaxiras 1996, Solid State Commun. 99, 57.