The ELPA library: Scalable parallel eigenvalue solutions for electronic structure theory and computational science

Journal of Physics Condensed Matter

Volumn 26, Issue 21, 2014, Pages

  Marek, A ^a   Blum, V ^b,c   Johanni, R ^a,b   Havu, V ^d   Lang, B ^e   Auckenthaler, T ^f   Heinecke, A ^f   Bungartz, H J ^f   Lederer, H ^a  

^a MAX PLANCK COMPUTING AND DATA FACILITY   (Germany)

^b FRITZ HABER INSTITUT DER MAX PLANCK GESELLSCHAFT   (Germany)

^c Duke University   (United States)

^d AALTO UNIVERSITY   (Finland)

^e UNIVERSITY OF WUPPERTAL   (Germany)

^f TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

density functional theory; eigenvalue solver; electronic structure theory; linear algebra

Indexed keywords

ALGORITHM; BIOLOGY; ELECTRONICS; MATHEMATICAL PHENOMENA;

ALGORITHMS; COMPUTATIONAL BIOLOGY; ELECTRONICS; MATHEMATICAL CONCEPTS;

EID: 84900454935     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/26/21/213201     Document Type: Review

References (79)

1. Boys S 1950 Electronic wave functions. II. A calculation for the ground state of the beryllium atom Proc. R. Soc. Lond. A 201 125
2. Nesbet R K 1965 Algorithm for diagonalization of large matrices J. Chem. Phys. 43 311
3. Golub G H and van der Vorst H A 2000 Eigenvalue computation in the 20th century J. Comput. Appl. Math. 123 35
4. Fock V 1930 Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems Z. Phys. 61 126
5. Roothaan C 1951 New developments in molecular orbital theory Rev. Mod. Phys. 23 69
6. Kohn W and Sham L 1965 Self-consistent equations including exchange and correlation effects Phys. Rev. 140 A1133
7. Blackford L et al 1997 ScaLAPACK Users' Guide (Philadelphia, PA: SIAM) (www.netlib.org/scalapack)
8. Davidson E R 1975 The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices J. Comput. Phys. 17 87
9. Wood D and Zunger A 1985 A new method for diagonalising large matrices J. Phys. A: Math. Gen. 18 1343
10. Knyazev A V 2001 Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method SIAM J. Sci. Comput. 23 517-41
11. Blaha P, Hofstätter H, Koch O, Laskowski R and Schwarz K 2010 Iterative diagonalization in augmented plane wave based methods in electronic structure calculations J. Comput. Phys. 229 453-60
12. Rayson M J 2010 Rapid filtration algorithm to construct a minimal basis on the fly from a primitive Gaussian basis Comput. Phys. Commun. 181 1051-56
13. Polizzi E 2009 Density-matrix-based algorithm for solving eigenvalue problems Phys. Rev. B 79 115112
14. Hine N D M, Haynes P D, Mostofi A, Skylaris C and Payne M C 2009 Linear-scaling density-functional theory with tens of thousands of atoms: expanding the scope and scale of calculations with ONETEP Comput. Phys. Commun. 180 1041-53
15. Bowler D R and Miyazaki T 2012 O(N) methods in electronic structure calculations Rep. Prog. Phys. 75 036503
16. VandeVondele J, Borstnik U and Hutter J 2012 Linear scaling self-consistent field calculations with millions of atoms in the condensed phase J. Chem. Theor. Comput. 8 3565
17. www.top500.org/
18. Alpatov P, Baker G, Edwards C, Gunnels J, Morrow G, Overfelt J, van de Geijn R and Wu Y-J 1997 PLAPACK: parallel linear algebra package: design overview Proc. Conf. on Supercomputing (SC97, July, 1997) Vienna
19. PLAPACK (www.cs.utexas.edu/users/plapack)
20. www.cs.utexas.edu/users/plapack/papers/icpp98.ps
21. Imamura T, Yamada S and Yoshida M 2011 Development of a high-performance eigensolver on a peta-scale next-generation supercomputer system Prog. Nucl. Sci. Technol. 2 643-50 www.aesj.or.jp/publication/pnst002/data/643-650.pdf
22. Auckenthaler T, Blum V, Bungartz H, Huckle T, Johanni R, Krämer L, Lang B, Lederer H and Willems P 2011 Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations Parallel Comput. 37 783-94
23. Poulson J, Marker B, van de Geijn R A, Hammond J A and Romero N A 2013 Elemental: a new framework for distributed memory dense matrix computations ACM Trans. Math. Softw. 39 13
24. Petschow M, Peise E and Bientinesi P 2013 High-performance solvers for dense Hermitian eigenproblems SIAM J. Sci. Comput. 35 C1-22
25. www.aics.riken.jp/labs/lpnctrt/EigenExa-e.html
26. http://icl.cs.utk.edu/plasma
27. Haidar A, Solca R, Gates M, Tomov S, Schulthess T and Dongarra J 2013 Leading edge hybrid multi-GPU algorithms for generalized eigenproblems in electronic structure calculations Int. Supercomputing Conf. (LeipzigBerlin: Springer, June 2013) ed Kunkel J M 67-80 Lecture Notes in Computer Science vol 7905
28. http://icl.utk.edu/magma
29. http://elpa.rzg.mpg.de
30. Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X, Reuter K and Scheffler M 2009 Ab initio 180 2175-96 molecular simulations with numeric atom-centered orbitals Comput. Phys. Commun.
31. Havu V, Blum V, Havu P and Scheffler M 2009 Efficient O(N) integration for all-electron electronic structure calculation using numeric basis functions J. Comput. Phys. 228 8367-79
32. http://aims.fhi-berlin.mpg.de
33. Havu P, Blum V, Havu V, Rinke P and Scheffler M 2010 Large-scale surface reconstruction energetics of Pt(1 0 0) and Au(1 0 0) by all-electron density functional theory Phys. Rev. B 82 161418
34. Nemec L, Blum V, Rinke P and Scheffler M 2013 Thermodynamic equilibrium conditions of graphene films on SiC Phys. Rev. Lett. 111 065502
35. Anderson E et al 1999 3rd edn (Philadelphia, PA: SIAM) www.netlib.org/lapack
36. Hutter J, Iannuzzi M, Schiffmann F and Vande Vondele J 2014 Cp2k: atomistic simulations of condensed matter systems Wiley Interdiscip. Rev. Comp. Mol. Sci. 4 15-25
37. Kresse G and Furthmüller J 1996 Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Comput. Mater. Sci. 6 15-50
38. Kresse G and Furthmüller J 1996 Efficient iterative schemes for ab initio B 54 11169 total-energy calculations using a plane-wave basis set
39. Giannozzi P et al 2009 Quantum espresso: a modular and open-source software project for quantum simulations of materials J. Phys.: Condens. Matter 21 395502
40. Yachmenev A, Polyak I and Thiel W 2013 Theoretical rotation-vibration spectrum of thioformaldehyde J. Chem. Phys. 139 204208
41. Golub G H and Loan C F V 2012 Matrix Computations ((Baltimore, MD: John Hopkins University Press)
42. Bischof C, Lang B and Sun X 1994 Parallel tridiagonalization through two-step band reduction (Los Alamitos, CA: IEEE Computer Society Press) 23-7
43. Bischof C H, Lang B and Sun X 2000 A framework for symmetric band reduction ACM Trans. Math. Softw. 26 581-601
44. Bischof C H, Lang B and Sun X 2000 Algorithm 807: the SBR toolbox - software for successive band reduction ACM Trans. Math. Softw. 26 602-16
45. Francis J G F 1961/1962 The QR transformation: a unitary analogue to the LR transformation, parts I and II Comput. J. 4 265-71 332-45
46. Demmel J W and Stanley K S 1994 The performance of finding eigenvalues and eigenvectors of dense symmetric matrices on distributed memory computers (Philadelphia, PA: SIAM) 528-33
47. Demmel J W 1997 Applied Numerical Linear Algebra (Philadelphia, PA: SIAM)
48. Cuppen J J M 1981 A divide and conquer method for the symmetric tridiagonal eigenproblem Numer. Math. 36 177-95
49. Gu M and Eisenstat S C 1995 A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem SIAM J. Matrix Anal. Appl. 16 172-91
50. Tisseur F and Dongarra J J 1999 A parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures SIAM J. Sci. Comput. 20 2223-36
51. Dhillon I S 1997 A new O(n2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem PhD Thesis University of California, Berkeley
52. Bientinesi P, Dhillon I S and Geijn R A V D 2005 A parallel eigensolver for dense symmetric matrices based on multiple relatively robust representations SIAM J. Sci. Comput. 27 43-66
53. Willems P R 2010 On MR3-type algorithms for the tridiagonal symmetric eigenproblem and the bidiagonal SVD PhD Thesis Bergische Universität Wuppertal
54. Willems P R and Lang B 2013 A framework for the MR3 algorithm: theory and implementation SIAM J. Sci. Comput. 35 A740-66
55. Haidar A, Ltaief H and Dongarra J 2012 Toward a high performance tile divide and conquer algorithm for the dense symmetric eigenvalue problem SIAM J. Sci. Comput. 34 C249-74
56. Gansterer W N, Schneid J and Ueberhuber C W 2001 A low-complexity divide-and-conquer method for computing eigenvalues and eigenvectors of symmetric band matrices BIT 41 967-76
57. König G, Moldaschl M and Gansterer W N 2012 Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations J. Comput. Appl. Math. 236 3696-703
58. Ballard G, Demmel J and Knight N 2013 Avoiding communication in successive band reduction Technical Report UCB/EECS-2013-131 EECS Department, University of California, Berkeley
59. Blackford L S et al 2002 An updated set of basic linear algebra subprograms (BLAS) ACM Trans. Math. Softw. 28 135-51
60. Dongarra J 2002 Basic linear algebra subprograms technical (BLAST) forum standard Int. J. High Perform. Comput. Appl. 16 1-111
61. Dongarra J 2002 Basic linear algebra subprograms technical (BLAST) forum standard Int. J. High Perform. Comput. Appl. 16 115-99
62. Clint Whaley R et al http://math-atlas.sourceforge.net
63. Goto K www.tacc.utexas.edu/tacc-software/gotoblas2
64. Openblas http://xianyi.github.com/OpenBLAS
65. Wan Q, Zhang X, Zhang Y and Qing Y 2013 AUGEM: automatically generate high performance dense linear algebra kernels on x86 CPUs Int. Conf. High Performance Computing, Networking, Storage and Analysis SC'13 (Denver,) (Piscataway, NJ: IEEE)
66. Breitmoser E and Sunderland A G 2003 A performance study of the PLAPACK and ScaLAPACK eigensolvers on hpcx for the standard problem Technical Report from the HPCx Consortium www.hpcx.ac.uk/research/hpc/HPCxTR0406.pdf (retrieved December 2013)
67. Balay S, Gropp W D, McInnes L C and Smith B F 1997 Efficient management of parallelism in object oriented numerical software libraries Modern Software Tools in Scientific Computing ed Arge E et al (Boston, MA: Birkhäuser) pp 163-202
68. Balay S, Brown J, Buschelman K, Gropp W D, Kaushik D, Knepley M G, McInnes L C, Smith B F and Zhang H 2013 PETSc Webpage www.mcs.anl.gov/petsc
69. Balay S, Brown J, Buschelman K, Eijkhout V, Gropp W D, Kaushik D, Knepley M G, McInnes L C, Smith B F and Zhang H 2013 PETSc users manual Technical Report ANL-95/11-Revision 3.4, Argonne National Laboratory
70. www.grycap.upv.es/slepc
71. Baker C G, Hetmaniuk U L, Lehoucq R B and Thornquist H K 2009 Anasazi software for the numerical solution of large-scale eigenvalue problems ACM Trans. Math. Softw. 36 1-23 13
72. Heroux M A et al 2005 An overview of the trilinos project ACM Trans. Math. Softw. 31 397-423
73. Gutheil I, Münchhalfen J F and Grotendorst J 2013 Performance of dense eigensolvers on BlueGene/Q 10th Int. Conf. on Parallel Processing and Applied Mathematics submitted
74. Imamura T www.aics.riken.jp/labs/lpnctrt/EigenExa-e.html
75. Demmel J W, Heath M T and van der Vorst H A 1993 Parallel numerical linear algebra LAPACK Working Note 60 UT CS-93-192 www.netlib.org/lapack/ lawnspdf/lawn60.pdf
76. Schweizer S, Kussmann J, Doser B and Ochsenfeld C 2008 Linear-scaling Cholesky decomposition Comput. Chem. 29 1004
77. Auckenthaler T, Huckle T and Wittmann R 2014 A blocked QR-decomposition for the parallel symmetric eigenvalue problem Parallel comput at press
78. Johanni R, Marek A, Lederer H and Blum V 2011 Scaling of eigenvalue solver dominated simulations Jülich BlueGene/P Extreme Scaling Workshop (Jülich, 2011) ed Mohr B and Frings W 27
79. Sunderland A 2012 Numerical library eigensolver performance on PRACE Tier-0 systems http://prace-ri.eu/IMG/pdf/numerical-library-eigensolver- performance-on-prace-tier-0-systems.pdf