Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

Journal of Computational Chemistry

Volumn 37, Issue 4, 2016, Pages 448-459

  Keçeli, Murat ^a   Zhang, Hong ^a   Zapol, Peter ^a   Dixon, David A ^b   Wagner, Albert F ^a  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF ALABAMA   (United States)

Author keywords

generalized eigenvalue problem; semi empirical methods; sparse matrices; spectrum slicing; tight binding DFT

Indexed keywords

BINS; CARBON; HAMILTONIANS; MATRIX ALGEBRA; NANOTUBES; PARALLEL ARCHITECTURES; SINGLE-WALLED CARBON NANOTUBES (SWCN); SWITCHING SYSTEMS; YARN;

GENERALIZED EIGENVALUE PROBLEMS; SEMI-EMPIRICAL METHODS; SPARSE MATRICES; SPECTRUM SLICING; TIGHT BINDING;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84953837379     PISSN: 01928651     EISSN: 1096987X     Source Type: Journal    
DOI: 10.1002/jcc.24254     Document Type: Article

References (80)

1. Kalil, T.,;, Wadia, C., Materials Genome Initiative for Global Competitiveness http://www.whitehouse.gov/sites/default/files/microsites/ostp/materials-genome-initiative-final. pdf (accessed Feb 12, 2015).
2. J. C. Slater, G. F. Koster, Phys. Rev. 1954, 94, 1498.
3. W. Foulkes, R. Haydock, Phys. Rev. B 1989, 39, 12520.
4. M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, T. Frauenheim, S. Suhai, G. Seifert, Phys. Rev. B 1998, 58, 7260.
5. G. Seifert, J Phys. Chem. A 2007, 111, 5609.
6. J. A. Pople, D. P. Santry, G. Segal, J. Chem. Phys. 1965, 43, S129.
7. M. J. S. Dewar, W. Thiel, J. Am. Chem. Soc. 1977, 99, 4899.
8. J. J. P. Stewart, J. Comput. Chem. 1989, 10, 209.
9. W. Thiel, Wiley Interdiscip. Rev. Comput. Mol. Sci. 2014, 4, 145.
10. R. J. Bartlett, M. Musiał, Rev. Mod. Phys. 2007, 79, 291.
11. P. Hohenberg, W. Kohn, Phys. Rev. 1964, 136, B864.
12. W. Kohn, L. Sham, J. Phys. Rev. 1965, 140, A1133.
13. P. C. Redfern, P. Zapol, L. A. Curtiss, K. Raghavachari, J. Phys. Chem. A 2000, 104, 5850.
14. S. Grimme, Org. Lett. 2010, 12, 4670.
15. J. E. Ridley, M. C. Zerner, Theor. Chim. Acta 1976, 42, 223.
16. Zerner, M. C., In Reviews in Computational Chemistry;, K. B. Lipkowitz, D. B. Boyd, Eds.; Wiley-VCH, Inc., 1991; pp 313-365.
17. M. Svensson, S. Humbel, R. D. J. Froese, T. Matsubara, S. Sieber, K. Morokuma, J Phys. Chem. 1996, 100, 19357.
18. Vreven, T.,;, Morokuma, K., In Annual Reports in Computational Chemistry;, D. C. Spellmeyer, Ed.; Elsevier: Amsterdam, 2006; Vol. 2, pp 35-51.
19. Gao, J., In Reviews in Computational Chemistry;, K. B. Lipkowitz, D. B. Boyd, Eds.; VCH Publishers, Inc.: New York, 2007; pp 119-185.
20. H. Zhang, B. Smith, M. Sternberg, P. Zapol, ACM Trans. Math. Softw. 2007, 33, 9.
21. C. Campos, J. E. Román, Numer. Algorithms 2012, 60, 279.
22. a. Marek, V. Blum, R. Johanni, V. Havu, B. Lang, T. Auckenthaler, a. Heinecke, H. J. Bungartz, H. Lederer, J Phys. Condens. Matter 2014, 26, 213201.
23. H. M. Aktulga, L. Lin, C. Haine, E. G. Ng, C. Yang, Parallel Comput. 2014, 40, 195.
24. D. Zuev, E. Vecharynski, C. Yang, N. Orms, A. I. Krylov, J. Comput. Chem. 2015, 36, 273.
25. M. Elstner, G. Seifert, Philos. Trans. R. Soc. A 2014, 372, 20120483.
26. W. Yang, Phys. Rev. Lett. 1991, 66, 1438.
27. A. D. Daniels, G. E. Scuseria, J. Chem. Phys. 1999, 110, 1321.
28. S. Goedecker, Rev. Mod. Phys. 1999, 71, 1085.
29. D. R. Bowler, T. Miyazaki, Reports Prog. Phys. 2011, 036503, 84.
30. L. Lin, A. García, G. Huhs, C. Yang, J. Phys. Condens. Matter 2014, 26, 305503.
31. C. Lanczos, J Res. Natl. Bur. Stand. (1934). 1950, 45, 255.
32. G. L. G. Sleijpen, H. A. Van der Vorst, SIAM Rev. 2000, 42, 267.
33. T. Ericsson, A. Ruhe, Math. Comput. 1980, 35, 1251.
34. J. J. Sylvester, Philos. Mag. IV 1852, 4, 138.
35. Balay, S.,;, Gropp, W. D. W.,;, McInnes, L. C. L.,;, Smith, B. F. B., In Modern Software Tools in Scientific Computing;, E. Arge, A. M. Bruaset, H. P. Langtangen, Eds.; Birkhäuser Press, 1997; pp 163-202.
36. S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, K. Rupp, B. F. Smith, H. Zhang, PETSc Users Manual, ANL-95/11-Revision 3.5 2014
37. V. Hernandez, J. E. Román, V. Vidal, ACM Trans. Math. Softw. 2005, 31, 351.
38. C. Campos, J. E. Román, E. Romero, A. Tomás, SLEPc Users Manual, DSIC-II/24/02-Revison 3.5 2014
39. P. R. Amestoy, I. S. Duff, J. Y. L'Excellent, J. Koster, SIAM J. Matrix Anal. Appl. 2001, 23, 15.
40. P. R. Amestoy, A. Guermouche, J. Y. L'Excellent, S. Pralet, Parallel Comput. 2006, 32, 136.
41. G. Karypis, V. Kumar, SIAM J. Sci. Comput. 1998, 20, 359.
42. G. Karypis, V. Kumar, J Parallel Distrib. Comput. 1998, 48, 71.
43. C. Chevalier, F. Pellegrini, Parallel Comput. 2008, 34, 318.
44. W. Gropp, E. Lusk,. In Proceedings of Scalable Parallel Libraries Conference; IEEE Comput. Soc. Press, 1993; pp 160-165.
45. R. B. Lehoucq, D. C. Sorensen, C. Yang, Communication 1998, 6, 147.
46. Argonne Leadership Computing Facility https://www.alcf.anl.gov/user-guides/mira-cetus-vesta (accessed Mar 7, 2015).
47. The vacuum space applied for the nanowire examples was not large enough to prevent interactions with images. Please see the Supporting Information for more details.
48. B. Aradi, B. Hourahine, T. Frauenheim, J Phys. Chem. A 2007, 111, 5678.
49. For our examples, carbon atoms have 4 valence electrons and 4 orbitals/atom so one-half of the orbitals are doubly occupied, but, for an example for water clusters, two-thirds of the orbitals are doubly occupied.
50. Pissanetzky, S., Sparse Matrix Technology, 1st ed.; Academic Press: London, 1984.
51. M. Yannakakis, SIAM J. Algebr. Discret. Methods 1981, 2, 77.
52. E. Cuthill, J. McKee,. In Proceedings of the 1969 24th national conference; ACM Press: New York, NY, USA, 1969; pp 157-172.
53. A. J. George,. Computer implementation of the finite element procedure, PhD Dissertation, Stanford University, Stanford, CA, 1971.
54. J. R. Gilbert, C. Moler, R. Schreiber, SIAM J. Matrix Anal. Appl. 1992, 13, 333.
55. Patrick Amestoy, Maurice Bremond, Alfredo Buttari, A. G.,;, Guillaume Joslin, Jean-Yves L'Excellent, Francois-Henry Rouet, B.,;, Weisbecker, U., and C. MUltifrontal Massively Parallel Solver (MUMPS) Version 4.10.0 http://mumps.enseeiht.fr /(accessed Dec 1, 2014).
56. A. George, SIAM J. Numer. Anal. 1973, 10, 345.
57. J. Poulson,. Fast parallel solution of heterogeneous 3D time-harmonic wave equations, PhD. Dissertation, The University of Texas at Austin, 2013.
58. A numerical factorization for the BDC64000 example cannot be performed on one core due to memory limitations.
59. G. M. Amdahl,. In Proceedings of the AFIPS spring joint computer conference SE-AFIPS '67 (Spring); 1967; pp 483-485.
60. A. Scemama, N. Renon, M. Rapacioli, J. Chem. Theory Comput. 2014, 10, 2344.
61. C. L. Janssen, I. M. B. Nielsen,. Parallel Computing in Quantum Chemistry, 1st ed.; CRC Press, Taylor & Francis Group: Boca Raton, FL, 2008.
62. M. Petschow, E. Peise, P. Bientinesi, SIAM J. Sci. Comput. 2013, 35, C1.
63. J. Poulson, B. Marker, R. A. van de Geijn, J. R. Hammond, N. A. Romero, ACM Trans. Math. Softw. 2013, 39, 1.
64. Gutheil, I.,;, Münchhalfen, J.,;, Grotendorst, J., In Parallel Processing and Applied Mathematics SE-3;, Wyrzykowski, R., Dongarra, J., Karczewski, K., Was̈niewski, J., Eds.; Lecture Notes in Computer Science; Springer Berlin Heidelberg, 2014; pp 26-35.
65. J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, R. C. Whaley, Comput. Phys. Commun. 1996, 97, 1.
66. Due to the large computational cost of loading matrices into Elemental, we couldn't perform calculations with more than 32,000 basis functions.
67. J. J. P. Stewart, P. Császár, P. Pulay, J. Comput. Chem. 1982, 3, 227.
68. D. R. Bowler, T. Miyazaki, J. Phys. Condens. Matter 2010, 22, 074207.
69. E. Rudberg, E. H. Rubensson, P. Sałek, J. Chem. Theory Comput. 2011, 7, 340.
70. J. VandeVondele, U. Borštnik, J. Hutter, J. Chem. Theory Comput. 2012, 8, 3565.
71. E. G. Birgin, J. M. Martínez, L. Martínez, G. B. Rocha, J. Chem. Theory Comput. 2013, 9, 1043.
72. E. H. Rubensson, P. Sałek, J. Comput. Chem. 2005, 26, 1628.
73. Y. Saad, J. R. Chelikowsky, S. M. Shontz, SIAM Rev. 2010, 52, 3.
74. L. Lin, J. Lu, L. Ying, E. Weinan, Chin. Ann. Math. Ser. B 2009, 30, 729.
75. L. Lin, C. Yang, J. C. Meza, J. Lu, L. Ying, E. W. ACM Trans. Math. Softw. 2011, 37, 1.
76. L. Lin, C. Yang, J. Lu, L. Ying, W. E, SIAM J. Sci. Comput. 2011, 33, 1329.
77. L. Lin, M. Chen, C. Yang, L. He, J. Phys. Condens. Matter 2013, 25, 295501.
78. G. Schofield, J. R. Chelikowsky, Y. Saad, Comput. Phys. Commun. 2012, 183, 497.
79. H. M. Aktulga, C. Yang, E. G. Ng, P. Maris, J. P. Vary, Concurr. Comput. Pract. Exp. 2014, 26, 2631.
80. E. L. Briggs, C. T. Kelley, J. Bernholc,. Parallel implementation of electronic structure eigensolver using a partitioned folded spectrum method http://arxiv.org/abs/1502.07806 (accessed Mar 7, 2015).