An efficient curved-wire integral equation solution technique

Computation of currents on curved wires by integral equation methods is oft en inefficient when the structure is tortuous but the length of wire is not large relative to wavelength at the frequency of operation. The number of terms needed in an accurate piecewise straight model of a highly curved wir e can be large, yet, if the total length of wire is small relative to wavel ength, the current can be accurately represented by a simple linear functio n. In this paper, a new solution method for the curved-wire integral equati on is introduced. It is amenable to uncoupling of the number of segments re quired to accurately model the wire structure from the number of basis func tions needed to represent the current. This feature lends itself to high ef ficiency. The principles set forth can be used to improve the efficiency of most solution techniques applied to the curved-wire integral equation. New composite basis and testing functions are defined and constructed as linea r combinations of other commonly used basis and testing functions. We show how the composite basis and testing functions can lead to a reduced-rank ma trix, which can be computed via a transformation of a system matrix created from traditional basis and testing functions. Supporting data demonstrate the accuracy of the technique and its effectiveness in decreasing matrix ra nk and solution time for curved-wire structures.