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

DOI:
https://doi.org/10.1090/S0025-5718-1969-0238502-4

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 at and and exterior to the circular conductors with arbitrarily spaced centers and radii . If the smallest distance between each pair of conducting surfaces exceeds .1, the capacitance matrix for this system of conductors can be calculated to 6-place accuracy at a cost of about 15 seconds on the IBM 7044 computer.

**[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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DOI:
https://doi.org/10.1090/S0025-5718-1969-0238502-4

Article copyright:
© Copyright 1969
American Mathematical Society