Computation of Laplacian potentials by an equivalent-source method

Abstract

An algorithm for the computation of the solution to Laplace's equation in a 2-dimensional region is given in terms of equivalent sources on the boundary. The region may be of an arbitrary shape, and the boundary conditions may be an arbitrary combination of Dirichlet, Neumann and impedance types. The solution is obtained by a moment method, using either a step approximation to the source, or a piecewise-linear approximation. Point matching is used for testing the boundary conditions. Computer programs are available for the general problem, and some electromagnetic-field applications are discussed.List of symbols a, j8, y = arbitrary functions of c <x c = attenuation constant due to metallic losses r) = yX/z/e) = intrinsic impedance of a medium CT = equivalent flux source on curve C e = permittivity /x = permeability p -radius vector to a point (x, y) <$> = solution to Laplace's equation V F, = potential from strip of uniform source on AC, A,-= length of element AC,-of curve C c = length variable along curve C g = conductivity k = constant Iji = elements of matrix [/] n = outward unit vector normal to curve C u = unit vector tangential to curve C w = complex function x, y -co-ordinates of point in space z -x + Jy = complex variable C = capacitance D = electric-flux density E = electric-field intensity H = magnetic-field intensity / = current J = current density P = power • P-, = pulse function Q -electric charge R = resistance V = constant potential Z o = characteristic impedance of a transmission line * denotes a complex conjugate

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Application of Direct Trefftz-Kupradze Method in Hierarchical Capacitance Extraction Problem

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Quasi-TEM Analysis of Microwave Transmission Lines by the Finite-Element Method

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