Computing entries of the inverse of a sparse matrix using the FIND algorithm

Journal of Computational Physics

Volumn 227, Issue 22, 2008, Pages 9408-9427

  Li, S ^a   Ahmed, S ^b   Klimeck, G ^c   Darve, E ^a  

^a Stanford University   (United States)

^b Southern Illinois University at Carbondale   (United States)

^c Purdue University   (United States)

Author keywords

Gaussian elimination; Green's function; Nanotransistor; NEGF; Nested dissection; Sparse matrix

Indexed keywords

BOUNDARY CONDITIONS; ELECTRON BEAM LITHOGRAPHY; INVERSE PROBLEMS; MATRIX ALGEBRA; MOS DEVICES; MOSFET DEVICES; OXIDE SEMICONDUCTORS; TREES (MATHEMATICS);

DUAL GATES; GATE METALS; GAUSSIAN ELIMINATION; GREENS FUNCTION; METALOXIDE SEMICONDUCTOR FIELD-EFFECT TRANSISTOR (MOSFETS); NANO TRANSISTORS; NANOSCALE TRANSISTORS; NESTED DISSECTION; NONEQUILIBRIUM GREENS FUNCTION (NEGF); SPARSE MATRICES;

NANOTRANSISTORS;

EID: 52749085483     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.06.033     Document Type: Article

References (23)

1. Datta S. Nanoscale device modeling: the Green's function method. Superlattices and Microstructures 28 4 (2000) 253-278
2. Lake R., Klimeck G., Bowen R.C., and Jovanovic D. Single and multiband modeling of quantum electron transport through layered semiconductor devices. Journal of Applied Physics 81 (1997) 7845
3. Svizhenko A., Anantram M.P., Govindan T.R., and Biegel B. Two-dimensional quantum mechanical modeling of nanotransistors. Journal of Applied Physics 91 4 (2002) 2343-2354
4. Varah J. The calculation of the eigenvectors of a general complex matrix by inverse iteration. Mathmatics of Compution 22 (1968) 785-791
5. Peters G., and Wilkinson J. Linear Algebra. Handbook for Automatic Computation vol. II (1971), Springer-Verlag Chapter: The calculation of specified eigenvectors by inverse iteration, pp. 418-791.
6. Wilkinson J. Inverse iteration in theory and practice. Symposia Matematica vol. X (1972), Institutio Nationale di Alta Matematica Monograf, Bologna, Italy 361-379
7. Peters G., Wilkinson J., and iteration I. ill-conditioned equations and Newton's method. SIAM Review 21 (1979) 339-360
8. George A. Nested dissection of a regular finite-element mesh. SIAM Journal on Numerical Analysis 10 2 (1973) 345-363
9. K. Takahashi, J. Fagan, M.-S. Chin, Formation of a sparse bus impedance matrix and its application to short circuit study, in: 8th PICA Conference Proceedings, Minneapolis, Minn., 1973, pp. 63-69.
10. Erisman A.M., and Tinney W.F. On computing certain elements of the inverse of a sparse matrix. Numerical Mathematics 18 3 (1975) 177-179
11. Bowden K. A direct solution to the block tridiagonal matrix inversion problem. International Journal of General Systems 15 3 (1989) 185-198
12. Schröder J., and Trottenberg U. Reduction method for difference equations for boundary value problems. I. Numerische Mathematik 22 1 (1973) 37-68
13. J. Schröder, U. Trottenberg, K. Witsch, On fast Poisson solvers and applications, in: R. Bulirsch, R. Grigorieff, J. Schröder (Eds.), a Conference on Numerical Treatment of Differential Equations, 4-10 July 1976, Oberwolfach, West Germany, 1978, pp. 153-87.
14. Buzbee B.L., Golub G.H., and Nielson C.W. On direct methods for solving Poisson's equations. SIAM Journal on Numerical Analysis 7 4 (1970) 627-656
15. Wong H.S. Beyond the conventional transistor. IBM Journal of Research and Development 46 (2002) 133-168
16. Welser J., Hoyt J.L., and Gibbons J.F. NMOS and PMOS transistors fabricated in strained silicon/relaxed silicon-germanium structures. IEDM Technical Digest (1992) 1000
17. Vasileska D., and Ahmed S.S. Narrow-width SOI devices: the role of quantum mechanical size quantization effect and the unintentional doping on the device operation. IEEE Transactions on Electron Devices 52 (2005) 227
18. Shahidi G. SOI technology for the GHz era. IBM Journal of Research and Development 46 (2002) 121-131
19. Walls T.J., Sverdlov V.A., and Likharev K.K. Nanoscale SOI MOSFETs: a comparison of two options. Solid-State Electronics 48 (2004) 857-865
20. Hasan S., Wang J., and Lundstrom M. Device design and manufacturing issues for 10 nm-scale MOSFETs: a computational study. Solid-State Electronics 48 (2004) 867-875
21. S.I.A. (SIA), International Technology Roadmap for Semiconductors 2001 Edition, Semiconductor Industry Association (SIA), 2706 Montopolis Drive, Austin, Texas 78741 , 2001, Chapter: Table C, p. 32.
22. Svizhenko A., Anantram M.P., Govindan T., Biegel B., and Venugopal R. Two-dimensional quantum mechanical modeling of nanotransistors. Journal of Applied Physics 91 4 (2002) 2343-2354
23. M.P. Anantram, S.S. Ahmed, A. Svizhenko, D. Kearney, G. Klimeck, NanoFET, doi:10.254/nanohub-r1090.5, 2007.