Quasi 3-D moment method for rapid calculation of electric field distribution in a low loss inhomogeneous dielectric

Abstract

Numerous applications of dielectric modelling require computation of the distribution of the total electric field in an inhomogeneous dielectric, in response to an applied electric field. An integral equation method would normally use an electric field volume integral technique using the moment method and hence compute the field in three-dimensional space. For those instances where the third dimension of the region is invariant, the heavy resource use of calculating the additional dimension is an unnecessary burden. The revised method reported in this paper sums the field contribution from the invariant third dimension at each stage of the two dimensional calculation, reducing the order of the model matrix by 4n² where n is the number of cells in each dimension. Thus by accepting a small loss in accuracy of less than 3 %, this procedure reduces the required memory resource by more than 4n², and execution time is dramatically improved. Assuming an essentially loss less permittivity, we use the calculated electric field distribution from a parallel transmission line to calculate the line's propagation velocity, and demonstrate favourable comparison with measured values.