A hybrid method for the parallel computation of Green's functions

Journal of Computational Physics

Volumn 228, Issue 14, 2009, Pages 5020-5039

  Petersen, Dan Erik ^a   Li, Song ^b   Stokbro, Kurt ^a   Sørensen, Hans Henrik B ^c   Hansen, Per Christian ^d   Skelboe, Stig ^a   Darve, Eric ^b  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b Stanford University   (United States)

^c AARHUS UNIVERSITY   (Denmark)

^d TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Cyclic reduction; Density functional theory; Green's function; Inverse matrix; Nested dissection; Parallel computing; Quantum transport; Sparse matrix

Indexed keywords

COMPUTATION THEORY; INVERSE PROBLEMS; MATRIX ALGEBRA; PARALLEL PROCESSING SYSTEMS; QUANTUM CHEMISTRY; QUANTUM ELECTRONICS; SUPERCOMPUTERS;

CYCLIC REDUCTION; DENSITY-FUNCTIONAL-THEORY; FUNCTION MATRIXES; GREENS FUNCTION; HYBRID METHOD; INVERSE-MATRIX; NESTED DISSECTION; PARALLEL COM- PUTING; QUANTUM TRANSPORT; SPARSE MATRICES;

DENSITY FUNCTIONAL THEORY;

EID: 67349099906     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.03.035     Document Type: Article

References (22)

1. International technology roadmap for semiconductors, , 2007.
2. Shankar S., Simka H., and Haverty M. Density functional theory and beyond - opportunities for quantum methods in materials modeling semiconductor technology. J. Phys.: Condens. Matter 20 (2008) 64232-64240
3. Friedman R.S., McAlpine M.C., Ricketts D.S., Ham D., and Lieber C.M. Nanotechnology: high-speed integrated nanowire circuits. Nature 434 (2005) 1085
4. Appenzeller J., Lin Y.-M., Knoch J., and Avouris P. Band-to-band tunneling in carbon nanotube field-effect transistors. Phys. Rev. Lett. 93 19 (2004) 196805. http://dx.doi.org/10.1103/PhysRevLett.93.196805 10.1103/PhysRevLett.93.196805
5. Ben-Jacob E., Hermon Z., and Caspi S. DNA transistor and quantum bit element: realization of nano-biomolecular logical devices. Phys. Lett. A 263 (1999) 199-202
6. Kubatkin S., Danilov A., Hjort M., Cornil J., Bredas J.L., Stuhr-Hansen N., Hedegard P., and Björnholm T. Single-electron transistor of a single organic molecule with access to several redox states. Nature 425 (2003) 698
7. Datta S. Electronic Transport in Mesoscopic Systems (1997), Cambridge University Press, Cambridge, UK
8. Haug H., and Jauho A.-P. Quantum Kinetics in Transport and Optics of Semiconductors (1996), Springer-Verlag, Berlin
9. Brandbyge M., Mozos J.-L., Ordejón P., Taylor J., and Stokbro K. Density-functional method for nonequilibrium electron transport. Phys. Rev. B 65 16 (2002) 165401 10.1103/PhysRevB.65.165401
10. Svizhenko A., Anantram M.P., Govindan T.R., Biegel B., and Venugopal R. Two-dimensional quantum mechanical modeling of nanotransistors. J. Appl. Phys. 91 4 (2002) 2343-2354
11. K. Takahashi, J. Fagan, M.-S. Chin, Formation of a sparse bus impedance matrix and its application to short circuit study, in: Eigth PICA Conference on Proceedings, Minneapolis, MN, 1973, pp. 63-69.
12. Erisman A.M., and Tinney W.F. On computing certain elements of the inverse of a sparse matrix. Numer. Math. 18 3 (1975) 177-179
13. Niessner H., and Reichert K. On computing the inverse of a sparse matrix. Int. J. Numer. Meth. Eng. 19 (1983) 1513-1526
14. Li S., Ahmed S., Klimeck G., and Darve E. Computing entries of the inverse of a sparse matrix using the FIND algorithm. J. Comput. Phys. 227 22 (2008) 9408-9427. http://dx.doi.org/10.1016/j.jcp.2008.06.033 doi: http://dx.doi.org/10.1016/j.jcp.2008.06.033
15. Schröder J. Zur lösung von potentialaufgaben mit hilfe des differenzenverfahrens. Angew. Math. Mech. 34 (1954) 241-253
16. Hageman L.A., and Varga R.S. Block iterative methods for cyclically reduced matrix equations. Numerische Mathematik 6 (1964) 106-119
17. George A. Nested dissection of a regular finite-element mesh. SIAM J. Numer. Anal. 10 2 (1973) 345-363
18. S. Li, E. Darve, Opimation of the FIND algorithm to compute the inverse of a sparse matrix, in: 13th International Workshop on Computational Electronics, 27-29 May, Beijing, China, 2009.
19. W. Gander, G.H. Golub, Cyclic reduction - history and applications, in: Scientific Computing: Proceedings of the Workshop 10-12 March 1997, pp. 73-85.
20. Heller D. Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems. SIAM J. Num. Anal. 13 4 (1976) 484-496
21. Golub G.H., and Loan C.F.V. Matrix Computations. third ed. (1996), Johns Hopkins University Press
22. D.E. Petersen, Block tridiagonal matrices in electronic structure calculations, Ph.D. Thesis, Dept. of Computer Science, Copenhagen University, 2008.