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Numerical solution of the Dirichlet problem for systems of circular conductors between parallel ground lines

Author: David W. Kammler
Journal: Math. Comp. 23 (1969), 29-36
MSC: Primary 65.66
MathSciNet review: 0238502
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Abstract: A Green's function-integral equation technique is used to obtain a numerical solution to the two-dimensional Dirichlet problem for the multiply connected region between the ground fines $ (V = 0)$ at $ y = 0$ and $ y = 1$ and exterior to the $ N$ circular conductors with arbitrarily spaced centers $ ({x_i},{y_i})$ and radii $ {R_i},i = 1,2, \cdots ,N$ . If the smallest distance between each pair of conducting surfaces exceeds .1, the capacitance matrix for this system of $ N$ conductors can be calculated to 6-place accuracy at a cost of about 15 $ {N^2}$ seconds on the IBM 7044 computer.

References [Enhancements On Off] (What's this?)

  • [1] R. C. Knight, ``The potential of a circular cylinder between two infinite planes,'' Proc. London Math. Soc., v. 39, 1935, pp. 272-281.
  • [2] J. W. Craggs, The determination of capacity for two-dimensional systems of cylindrical conductors, Quart. J. Math., Oxford Ser. 17 (1946), 131–137. MR 0018534
  • [3] E. G. Cristal, ``Coupled circular cylindrical rods between parallel grounded planes,'' IEEE Trans., v. MTT-12, 1964, pp. 422-439.
  • [4] O. D. Kellogg, Foundations of Potential Theory, Dover, New York, 1953.
  • [5] L. V. Bewley, Two Dimensional Fields in Electrical Engineering, Dover, New York, 1963, p. 159.
  • [6] James Clerk Maxwell, A treatise on electricity and magnetism, Dover Publications, Inc., New York, 1954. 3d ed; Two volumes bound as one. MR 0063293
  • [7] Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 0167642
  • [8] Herbert Bristol Dwight, Tables of integrals and other mathematical data, 4th ed, The Macmillan Company, New York, 1961. MR 0129577

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Article copyright: © Copyright 1969 American Mathematical Society