The capacitance of the cube and square plate by random walk methods

Journal of Electrostatics

Volumn 62, Issue 1, 2004, Pages 51-62

  Wintle, H J ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

Capacitance; Cube; Field calculation; Random walk; Square plate; Variational bounds

Indexed keywords

ERROR ANALYSIS; PLATE METAL; REDUCTION; VARIATIONAL TECHNIQUES;

RANDOM WALK METHOD; SQUARE PLATE; UPPER AND LOWER BOUND;

CAPACITANCE;

ELECTROSTATICS;

EID: 3242664963     PISSN: 03043886     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.elstat.2004.04.005     Document Type: Article

References (31)

1. Douglas J.F. Zhou H.-X. Hubbard J.B. Hydrodynamic friction and the capacitance of arbitrarily shaped objects Phys. Rev. E 49 1994 5319-5331 [The basis for the conjecture is given in their footnote [36]]
2. Polya G. Szego G. Isoperimetric Inequalities in Mathematical Physics 1951 Princeton University Press Princeton, NJ
3. A.M. Arthurs, Complementary Variational Principles, 2nd Edition, Clarendon, Oxford, 1980, pp. 65-66.
4. Weinstock R. Calculus of Variations 1952 McGraw-Hill New York [reissued by Dover, New York, 1974, Chapter 12]
5. Parr W.E. Upper and lower bounds for the capacitance of the regular solids J. Soc. Ind. Appl. Math. 9 1961 334-386
6. Payne L.E. Weinberger H.F. New bounds in harmonic and biharmonic problems J. Math. Phys. 33 1955 291-307
7. J.C. Maxwell, The Electrical Researches of the Hon. Henry Cavendish, F.R.S., Cambridge University Press, Cambridge, 1879, p. 426.
8. G.D. Cochran, Ph.D. thesis, University of Michigan, 1967, pp. 180-185.
9. Reitan D.K. Higgins T.J. Calculation of the electrical capacitance of a cube J. Appl. Phys. 22 1951 223-226
10. Van Bladel J. Electromagnetic Fields 1964 McGraw-Hill New York [reissued by Hemisphere, New York, 1985]
11. Mautz J.R. Harrington R.F. Computation of rotationally symmetric Laplacian potentials Proc. IEE 117 1970 850-852
12. Martinez G. Sancho M. Integral equation method in electrostatics Am. J. Phys. 51 1983 170-174
13. Morrison J.A. Lewis J.A. Charge singularity at the corner of a flat plate SIAM J. Appl. Math. 31 1976 233-250
14. Hanson R.J. Phillips J.L. Numerical solution of two-dimensional integral equations using linear elements SIAM J. Num. Anal. 15 1978 113-121
15. Ruehli A.E. Brennan P.A. Efficient capacitance calculations for three-dimensional multiconductor systems IEEE Trans. Microwave Ther. Tech. 21 1973 76-83
16. Hoole S.R.H. Computer-Aided Analysis and Design of Electromagnetic Devices 1989 Elsevier New York
17. Bettess P. Finite element modelling of exterior electromagnetic problems IEEE Trans. Magn. 24 1988 238-243
18. Aiello G. Alfonzetti S. Coco S. Charge iteration for n-dimensional unbounded electrical field computations IEEE Trans. Magn. 28 1992 1682-1685
19. Lowther D.A. Freeman E.M. Further aspects of the Kelvin transformation method for dealing with open boundaries IEEE Trans. Magn. 28 1992 1667-1670
20. Imhoff J.F. Meunier G. Sabonnadiere J.C. Finite element modeling of open boundary problems IEEE Trans. Magn. 26 1990 588-591
21. P. Moon, D.E. Spencer, Field Theory Handbook, 2nd Edition (corrected), Springer, Berlin, 1988, pp. 122-123.
22. Brown C.S. Capacity of the regular polyhedra Comput. Math. Appl. 20 1990 43-56
23. Wintle H.J. The capacitance of the regular tetrahedron and equilateral triangle J. Electrostat. 26 1991 115-120
24. Zhou H.-X. Szabo A. Douglas J.F. Hubbard J.B. A Brownian dynamics algorithm for calculating the hydrodynamic friction and the electrostatic capacitance of an arbitrarily shaped object J. Chem. Phys. 100 1994 3821-3826
25. E. Durand, Electrostatique, Vol. 2, Masson, Paris, 1966, pp. 210-211.
26. P. l'Ecuyer, Efficient and portable combined random number generators, Commun. ACM 31 (1988) 742-749 - 774.
27. 12]
28. Goto E. Shi Y. Yoshida N. Extrapolated surface charge method for capacity calculation of polygons and polyhedra J. Comput. Phys. 100 1992 105-115
29. Read F.H. Improved extrapolation technique in the boundary element method to find the capacitances of the unit square and cube J. Comput. Phys. 133 1997 1-5
30. S. Sato, Dissertation, ETH, Zurich, 1987, pp. 87-91, 195.
31. Wintle H.J. Maxwell and the boundary element method: a historical puzzle IEEE Electr. Insul. Mag. 14 6 1998 23-25