Reduced rank matrices for curved wire structures

Numerical solution techniques for curved wires typically require large matrices since the variation of the structure's geometry must be modeled accurately. This is clearly true when straight segments are used to approximate a curvilinear structure in which case the number of basis functions needed in solution methods often is dictated by the structure curvature more so than by the variation of the unknown function (current) itself. There is a need for a solution technique in which the number of unknowns necessary for an accurate solution of the current is not dictated by the number of straight segments required to represent the meandering contour of the wire and the vector direction of the current on it. A technique for reducing unknowns on curved wire structures (e.g. spiral or loop antennas) approximated by straight wire segments is described and supporting results are presented.