Separation of horizontal and vertical dependencies in a surface/volume integral equation approach to model quasi 3-D structures in multilayered media

A new and efficient integral equation approach is presented to model heterogeneous dielectric volumes in a multilayered environment. The dielectric volumes can be vertically large, they can cross dielectric interfaces and they should be '' quasi 3-D,'' which means that the contour faces should be placed either horizontally or vertically in the multilayered environment. In this way, a perpendicular prismatic mesh can be fitted on the volumes and the 3-D displacement currents can be expanded in generalized rooftop functions with separated horizontal x, y- and vertical z-dependencies. This makes it possible to evaluate all z, z' reaction integrals fully analytically in the spectral domain and ensures an efficient implementation. The formulation of the source-field relations is adapted to the quasi 3-D geometries as a hybrid dyadic-mixed potential form. Additionally, the electromagnetic coupling between dielectric volumes and metal sheets is included using a coupled volume/surface formulation. This turns the implementation into a complete full wave solver for planar antennas containing both finite and infinite dielectric regions. In order to illustrate and validate the presented approach, two patch antennas with a local volumetric inhomogeneity under the patch are numerically analyzed in a multilayered environment. Eventually, a matrix fill time comparison is used to demonstrate the improvement in computation efficiency.