A parallelized 3D floating random-walk algorithm for the solution of the nonlinear poisson-boltzmann equation

Progress in Electromagnetics Research

Volumn 57, Issue , 2006, Pages 237-252

  Chatterjee, K ^a,c   Poggie, J ^b  

^a The Cooper Union for the Advancement of Science and Art   (United States)

^b AIR FORCE RESEARCH LABORATORY   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947179861     PISSN: 10704698     EISSN: 15598985     Source Type: Journal    
DOI: 10.2528/PIER05072802     Document Type: Article

References (17)

1. Mitchner, M. and C. H. Kruger, Partially Ionized Gases, John Wiley & Sons, New York, 1973.
2. Sze, S. M., Physics of Semiconductor Devices, 2nd ed., 366-368, John Wiley & Sons, New York, 1999.
3. Davis, M. E. and J. A. McCammon, "Electrostatics in biomolecular structure and dynamics," Chemical Reviews, Vol. 90, 509-521, 1990.
4. Brown, G. M., Modern Mathematics for Engineers, E. F. Beckenbach (ed.), McGraw-Hill, New York, 1956.
5. Le Coz, Y. L., H. J. Greub, and R. B. Iverson, "Performance of random walk capacitance extractors for IC interconnects: a numerical study," Solid-State Electronics, Vol. 42, 581-588, 1998.
6. Le Coz, Y. L., R. B. Iverson, T. L. Sham, H. F. Tiersten, and M. S. Shepard, "Theory of a floating random walk algorithm for solving the steady-state heat equation in complex materially inhomogeneous rectilinear domains," Numerical Heat Transfer, Part B: Fundamentals, Vol. 26, 353-366, 1994.
7. Haberman, R., Elementary Applied Partial Differential Equations, 3rd ed., Prentice-Hall, Englewood Cliffs, NJ, 1998.
8. Hwang, C.-O. and M. Mascagni, "Efficient modified 'walk on spheres' algorithm for the linearized poisson-boltzmann equation," App. Phys. Lett., Vol. 78, No. 6, 787-789, 2001.
9. Mascagni, M. and N. A. Simonov, "Monte carlo methods for calculating the electrostatic energy of a molecule," Proceedings of the 2003 International Conference on Computational Science (ICCS 2003).
10. Chatterjee, K. and J. Poggie, "A meshless stochastic algorithm for the solution of the nonlinear poisson-boltzmann equation in the context of plasma discharge modeling: ID analytical benchmark," Proceedings of the 17th AIAA Computational Fluid Dynamics Conference, 2005-5339, Toronto, Ontario, Canada, June 6-9, 2005 (American Institute of Aeronautics and Astronautics, Reston, VA, 2005).
11. Chatterjee, K. and J. Poggie, "A two-dimensional floating random-walk algorithm for the solution of the nonlinear Poisson-Boltzmann equation: application to the modeling of plasma sheaths," Proceedings of the 3rd MIT Conference on Computational Fluid and Solid Mechanics, 1058-1061, Cambridge, MA, June 14-17, 2005 (Elsevier, Oxford UK, 2005).
12. Sobol, I. M., A Primer for the Monte Carlo Method, CRC Press, Boca Raton, 1994.
13. Curtiss, J. H., "Monte carlo methods for the iteration of linear operators," J. Math. and Phys., Vol. 32, 209-232, 1954.
14. Sabelfeld, K. K. and N. A. Simonov, Random Walks on Boundary for Solving PDEs, 119-120, VSP, Utrecht, The Netherlands, 1994.
15. Chatterjee, K., "Development of a floating random walk algorithm for solving Maxwell's equations in complex IC-interconnect structures," Rensselaer Polytechnic Institute, May, 2002, UMI Dissertation Services, 300 North Zeeb Road, P.O. Box 1346, Ann Arbor, Michigan 48106-1346, USA, UMI Number: 3045374, Web Address: www.il.proquest.com.
16. Chatterjee, K. and Y. L. Le Coz, "A floating random-walk algorithm based on iterative perturbation theory: solution of the 2D vector-potential maxwell-helmholtz equation," Applied Computational Electromagnetics Society Journal, Vol. 18, No. 1, 48-57, March 2003.
17. Hammersley, J. M. and D. C. Handscomb, Monte Carlo Methods, 50-54, John Wiley & Sons, New York, NY, 1964.