Block tridiagonal matrix formulation for inhomogeneous penetrable cylinders

Analysis of penetrable two-dimensional scatterers is accomplished without the need to generate and solve a dense method of moments (MoM) matrix as is customarily done in the context of the volume integral formulation. Instead of the dense matrix, a rigorous tridiagonal block matrix is generated, for which the computational complexity is O(N² ). In this new formulation, the body is divided into a set of arbitrarily shaped layers, where each layer interacts with only adjacent layers, in a similar fashion to domain decomposition methods used in the past in the context of differential equations. The ability to describe the problem via near-neighbour interactions only is gained by the introduction of a dual set of unknowns, i.e. both electric and magnetic equivalent sources defined over the interfaces between the layers. The interrelations between the two types of sources are lumped into a `black box´ matrix representation for each layer, analogous to a multiport Z-matrix description of a microwave network. When the layers are cascaded, these matrices serve as blocks within the augmented banded matrix for the entire scatterer. The matrix can be solved either in a recursive way, utilising the cascading concept to produce solutions to intermediate structures along the way, or by an iterative algorithm. The method is formulated entirely in the spatial domain, however an S-matrix spectral representation, incorporating incoming and outgoing waves of the same field across the interface of each layer, is also possible. Actual operation counts are shown