Adaptive projection subspace dimension for the thick-restart lanczos method

ACM Transactions on Mathematical Software

Volumn 37, Issue 3, 2010, Pages

  Yamazaki, Ichitaro ^a   Bai, Zhaojun ^a   Simon, Horst ^b   Wang, Lin Wang ^b   Wu, Kesheng ^b  

^a University of California Davis   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

Adaptive subspace dimension; Electronic structure calculation; Lanczos; Thick restart

Indexed keywords

ADAPTIVE SCHEME; ADAPTIVE SUBSPACES; EIGENSOLVERS; EIGENVALUE PROBLEM; ELECTRONIC STRUCTURE CALCULATION; HERMITIANS; LANCZOS; LANCZOS METHODS; OBJECTIVE FUNCTIONS; OPEN-SOURCE SOFTWARES; PRECONDITIONED CONJUGATE GRADIENT; QUANTUM DOT; THICK-RESTART;

CONJUGATE GRADIENT METHOD; EIGENVALUES AND EIGENFUNCTIONS; ELECTRONIC PROPERTIES; QUANTUM THEORY;

ELECTRONIC STRUCTURE;

EID: 77955416445     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1824801.1824805     Document Type: Article

References (22)

1. CALVETTI, D., REICHEL, L., AND SORENSEN, D. 1994. An implicitly restarted Lanczos method for large symmetric eigenvalue problems. Electro. Trans. Numer. Anal. 2, 1-21.
2. CANNING, A., WANG, L. W., WILLIAMSON, A., AND ZUNGER, A. 2000. Parallel empirical pseudopotential electronic structure calculations for million atom systems. J. Comput. Phys. 160, 1, 29-41.
3. CROUZEIX, M., PHILIPPE, B., AND SADKANE, M. 1994. The Davidson method. SIAM J. Sci. Comput. 15, 62-76.
4. DEMMEL, J. W. 1997. Applied Numerical Linear Algebra. SIAM, Philadelphia, PA.
5. LANCZOS, C. 1950. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Stand. 45, 255-281.
6. LEHOUCQ, R., SORENSEN, D., AND YANG, C. 1998. ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM, Philadelphia, PA. Software http://www.caam.rice.edu/software/ ARPACK/.
7. LI, J. AND WANG, L. 2004. First principle study of core/shell structure quantum dots. Appl. Phys. Lett. 84, 18, 2648-3650.
8. MORGAN, P. B. 1996. On restarting the Arnoldi method for large nonsymmetric eigenvalule problems. Math. Comput. 65, 215, 1213-1230.
9. PARLETT, B. N. 1998. The Symmetric Eigenvalue Problem. Classics in Applied Mathematics. SIAM, Philadelphia, PA.
10. PAYNE, M. C., TETER, M. P., ALLAN, D. C., ARIAS, T. A., AND JOANNOPOULOS, J. D. 1992. Iterative minimization techniques for ab-initio total energy calculations: Molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045-1097.
11. SAAD, Y. 1993. Numerical Methods for Large Eigenvalue Problems. Manchester University Press, Manchester, UK.
12. SCHRIER, J. AND WANG, L. 2006. A systematic first principles study of nanocrystal quantum-dot quantum wells. Phys. Rev. B 73, 245332-245337
13. SORENSEN, D. 1992. Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Mat. Anal. Appl. 13, 1, 357-385.
14. STATHOPOULOS, A. AND MCCOMBS, J. R. 2007. Nearly optimal preconditioned methods for Hermitian eigenproblems under limited memory. Part II: Seeking many eigenvalues. SIAM J. Sci. Comput. 29, 5, 2162-2188.
15. STATHOPOULOS, A., SAAD, Y., AND WU, K. 1998. Dynamic thick restarting of the Davidson and the implicitly restarted Arnoldi methods. SIAM J. Sci. Comput. 19, 227-245.
16. VÖMEL, C., TOMOV, S. Z.,MARQUES, O. A., CANNING, A.,WANG, L., AND DONGARRA, J. J. 2008. State-of-the-Art eigensolvers for electronic structure calculation of large scale nano-systems. J. Comput. Phys. 227, 15, 7113-7124.
17. WANG, L., CANNING, A., MARQUES, O., AND VOEMEL, C. 2008. The parallel energy scan (PESCAN) code. http://icl.cs.utk.edu/doe-nano/software/pescan/escan.
18. WANG, L. AND ZUNGER, A. 1994. Solving Schrodinger's equation around a desired energy: Application to silicon quantum dots. J. Chem. Phys. 100, 2394-2397.
19. WANG, L. AND ZUNGER, A. 1996. Pseudopotential theory of nanometer silicon quantum dots application to silicon quantum dots. In Semiconductor Nanocluster, P. Kamat and D. Meisel Eds., ACM, New York, NY, 161-207.
20. WU, K. AND SIMON, H. 2000a. Thick-Restart Lanczos method for large symmetric eigenvalue problems. SIAM J. Mat. Anal. Appl. 22, 602-616.
21. WU, K. AND SIMON, H. 2000b. TRLan user guide. Tech. rep. LBNL-43178, Lawrence Berkeley National Laboratory. Software http://crd.lbl.gov/kewu/trlan. html.
22. YAMAZAKI, I., WU, K., AND SIMON, H. 2008. a-TRLan user guide. Tech. rep. LBNL-1288E, Lawrence Berkeley National Laboratory. Software https://codeforge. lbl.gov/projects/trlan/.