A Broadband Volume Integral Formulation Based on Edge-Elements for Full-Wave Analysis of Lossy Interconnects

A new numerical fully three-dimensional (3-D) volume integral formulation for the electromagnetic analysis from static to microwave frequencies of penetrable materials (dielectric, eventually lossy, and conductors with finite conductivity) is here discussed. Its key feature is the introduction of a volumetric loop-star decomposition for treating piecewise homogeneous materials. The associated shape functions have been determined to decompose the volume current density in a solenoidal and a nonsolenoidal part, in analogy to the surface loop-star shape functions, used for modeling surface current densities on perfect electric conductors. The possibility of modeling volumetric ohmic and polarization current densities allows to compute in an accurate way the electromagnetic field in complex 3-D geometries, such as high speed interconnects, on a broad range of frequencies.