Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel

Applied Numerical Mathematics

Volumn 37, Issue 1-2, 2001, Pages 189-199

  Bendtsen, Claus ^a   Nielsen, Ole H ^a   Hansen, Lars B ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; PARALLEL PROCESSING SYSTEMS; PROBABILITY DENSITY FUNCTION; PROBLEM SOLVING;

NONLINEAR GENERALIZED EIGENVALUE PROBLEMS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0035311242     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(00)00038-6     Document Type: Article

References (27)

1. Anderson D.G. Iterative procedures for nonlinear integral equations. J. ACM. 12:(4):1965;547-560.
2. Björk Å. Numerical Methods for Least Squares Problems. 1996;SIAM, Philadelphia, PA.
3. Bramble J.H., Pasciak J.E., Knyazev A.V. A subspace preconditioning algorithm for eigenvector/eigenvalue computation. Adv. Comput. Math. 6:1996;159-189.
4. Calvetti D., Reichel L., Sorensen D.C. An implicitly restarted Lanczos method for large symmetric eigenvalue problems. Electron. Trans. Numer. Anal. 2:1994;1-21.
5. Crouzeix M., Philippe B., Sadkane M. The Davidson method. SIAM J. Comput. Sci. 15:(1):1994;62-76.
6. Davidson E.R. The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comput. Phys. 17:1975;87-94.
7. Davidson E.R. Monster matrices: their eigenvalues and eigenvectors. Comput. Phys. 7:(5):1993;519-522.
8. Descloux J., Fattebert J.-L., Gygi F. Rayleigh quotient iteration, an old recipe for solving modern large-scale eigenvalue problems. Comput. Phys. 12:(1):1998;22-27.
9. Goedecker S. Linear scaling electronic structure methods. Rev. Mod. Phys. 71:1999;1085-1123.
10. Kresse G., Furthmüller J. Efficiency iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B. 54:(16):1996;11 169-11 186.
11. Lai Y.-L., Lin K.-Y., Lin W.-W. An inexact inverse iteration for large sparse eigenvalue problems. Numer. Linear Algebra Appl. 4:(5):1997;425-437.
12. Liu D.C., Nocedal J. On the limited memory BFGS method for large scale optimization. Math. Programming. 45:1989;503-528.
13. Message Passing Interface Forum, MPI: A Message-Passing Interface Standard. 1995;Univ. of Tennessee, Knoxville, TN.
14. Morgan R.B., Scott D.S. Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices. SIAM J. Sci. Stat. Comput. 7:(3):1986;817-825.
15. Morgan R.B., Scott D.S. Preconditioning the Lanczos algorithm for sparse symmetric eigenvalue problems. SIAM J. Sci. Comput. 14:(3):1993;585-593.
16. Olsen J., Jørgensen P., Simons J. Passing the one-billion limit in full configuration-interaction (FCI) calculations. Chem. Phys. Lett. 169:(6):1990;463-472.
17. Parlett B.N. The Symmetric Eigenvalue Problem. 1998;SIAM, Philadelphia, PA.
18. Parr R.G., Yang W. Density-Functional Theory of Atoms and Molecules. 1989;Oxford University Press.
19. Pulay P. Convergence acceleration of iterative sequences. The case of SCF iteration. Chem. Phys. Lett. 73:(2):1980;393-398.
20. Reichel L., Gragg W.B. FORTRAN subroutines for updating the QR decomposition. ACM Trans. Math. Software. 16:1990;369-377.
21. Saad Y., Stathopoulos A., Chelikowsky J., Wu K., Ögüt. Solution of large eigenvalue problems in electronic structure calculations. BIT. 36:(3):1996;563-578.
22. Saad Y. Numerical Methods for Large Eigenvalue Problems. 1992;Manchester University Press.
23. Sleijpen G.L.G., Booten A.G.L., Fokkema D.R., van der Vorst H.A. Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT. 36:(3):1996;595-633.
24. Sleijpen G.L.G., van der Vorst H.A. A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl. 17:(2):1996;401-425.
25. Stathopoulos A., Saad Y., Wu K. Dynamic thick restarting of the Davidson and the implicitly restarted Arnoldi methods. SIAM J. Sci. Comput. 19:(1):1998;227-245.
26. Teter M.P., Payne M.C., Allan D.C. Solution of Schrödinger's equation for large systems. Phys. Rev. B. 40:(18):1989;12 255-12 263.
27. Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B. 41:(11):1990;7892-7895.