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

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.