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

Numerous applications of dielectric modeling 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 (3-D) space. For those instances where the third dimension of the region is assumed to be invariant, such as when determining the spatial sensitivity of a time-domain reflectometry sensor, the heavy resource use of calculating the additional dimension is an unnecessary burden. The new method reported in this paper sums the field contributions from the invariant third dimension at each stage of a two-dimensional (2-D) calculation, reducing the order of the model matrix by 2n² 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 2n²,and execution time is dramatically improved. Assuming an essentially lossless permittivity, we use the calculated electric field distribution from a parallel transmission line to calculate the line´s propagation velocity and demonstrate favorable comparison with measured values. Moisture content measurement is used as an example