Study of Statistical Approaches to the Solution of Linear Discrete and Integral Problems

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 50, Issue 9, 2003, Pages 1153-1161

  Maffezzoni, Paolo ^a   Brambilla, Angelo ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Laplace equation; Linear discrete problems; Linear integral problems; Random walk (RW) method

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; PROBLEM SOLVING; STATISTICAL METHODS;

LINEAR DISCRETE PROBLEMS;

LINEAR ALGEBRA;

EID: 0141862237     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2003.816304     Document Type: Article

References (19)

1. R. M. Bevensee, "Probabilistic potential theory applied to electrical engineering problems", Proc. IEEE, vol. 61, pp. 423-437, Apr. 1973.
2. G. M. Royer,"A Monte Carlo procedure for potential theory problems", IEEE Trans. Microwave Theory Tech., vol. MTT-19, pp. 813-818, Oct. 1971.
3. M. N. O. Sadiku,"Monte Carlo methods in an introductory electromagnetic course", IEEE Trans. Educ., vol. 33, no. 1, pp. 73-80, Feb. 1990.
4. G. E. Albert, "A general theory of stochastic estimates of the newmann series for the solutions of certain fredholm integral equations and related series", in Symposium of Monte Carlo Methods, M. A. Meyer, Ed. New York: Wiley, 1956, pp. 37-46.
5. R. Y. Rubistain, Simulation and the Monte Carlo Method. New York: Wiley, 1981.
6. S. E. Forsythe and R. A. Leibler, "Matrix inversion by a Monte Carlo method", Math. Tables Other Aids Comput., no. 4, pp. 127-129, 1950.
7. P. Maffezzoni and A. Brambilla, "An efficient method to simulate time delays of distributed interconnections in VLSI circuits", Electron. Lett., vol. 35, no. 12, pp. 976-977, 1999.
8. A. Brambilla and P. Maffezzoni, "Statistical method for the analysis of interconnects delay in submicron layouts", IEEE Trans. Computer-Aided Design, vol. 20, pp. 957-966, Aug. 2001.
9. Y. L. Le Coz and R. B. Iverson, "A stochastic algorithm for high speed capacitance extraction in integrated circuits", Solid-State Electron., vol. 35, no. 7, pp. 1005-1012, 1992.
10. A. Brambilla and P. Maffezzoni, "A statistical algorithm for 3-D capacitance extraction", IEEE Microwave Guided Waves Lett., vol. 10, pp. 304-306, Aug. 2000.
11. K. Nabors, S. Kim, and J. White, "Fast capacitance extraction of general three-dimensional structures", IEEE Trans. Microwave Theory Tech., vol. 40, pp. 1496-1506, July 1992.
12. J. Stoer, Einfuhrung in die Numerische Mathematik. New York: Springer Verlag, 1972.
13. R. Courant and D. Hilbert, Methods of Mathematical Physics. New York: Interscience Publishers, 1966.
14. R. B. Iverson and Y. L. Le Coz, User Guide for QuickCap Version 3.0. Fairfax, VA: Random Logic Corp.
15. M. N. O. Sadiku, S. O. Ajose, and Z. Fu, "Applying the Exodus method to solve Poisson's equation", IEEE Trans. Microwave Theory Tech., vol. 42, pp. 661-666, Apr. 1994.
16. M. Sancho, J. L. Sebastian, S. Munoz, and J. M. Mirandam, "Computational method in electrostatics based on Monte Carlo energy minimization", Proc. Inst. Elect. Eng., Sci., Measur., Technol., vol. 148, no. 3, pp. 121-124, 2001.
17. M. N. O. Sadiku and D. Hunt, "Solution of dirichlet problems by the Exodus method", IEEE Trans. Microwave Theory Tech., vol. 40, pp. 89-95, Jan. 1992.
18. M. N. O. Sadiku, "Monte Carlo solution of axisymmetric potential problems", IEEE Trans. Ind. Applicat., vol. 29, pp. 1042-1046, Nov./Dec. 1993.
19. M. N. O. Sadiku and R. C. Garcia, "Whole field computation using Monte Carlo method", Int. J. Numer. Model., vol. 10, pp. 303-312, 1997.