A finite difference approach to the wire junction problem

An approach to treating the thin-wire junction geometry, which arises in the computer modeling of a great many electromagnetic radiation and scattering problems, is presented. The method is based upon a finite-difference type interpretation of the differential operator in the Pocklington form of the integro-differential equation representing the junction problem. An important advantage of the method is that it is capable of producing accurate results even with relatively simple basis and testing functions, e.g., pulse and\delta-functions. Furthermore, the method does not require the imposition of additional constraints, such as the Kirchhoff current law or the conservation of charge, at the junction points. The method is versatile in that it applies to L-shaped structures as well as to junctions of thin wires of dissimilar radii. Numerical results based on the present finite difference approach have been computed and good agreement with results derived by other independent methods has been observed. An important conclusion of this work is that the conventional interpretation of the differential operator leads to erroneous results since the sampling interval in the conventional finite difference scheme is different from the correct value of the sampling interval found in this paper.