Singular analytical integration for efficient Volume Integral Equation implementation

We present a novel efficient implementation of the Volume Integral Equation formulation, for the analysis of printed circuits with finite size dielectric objects. The singularity of the Green's functions is extracted from the kernel of the integral equation, as static terms. These terms are then evaluated analytically for coincident rectangular cells in two and three dimensions. A semi-analytical formulation is also derived for the interactions involving adjacent cells. Results show the gain in efficiency and accuracy that can be obtained in the frame of the Volume Integral Equation formulation, when the new analytical techniques are used.