Solving wave propagation within finite-sized composite media with linear embedding via Green's operators

The calculation of electromagnetic (EM) fields and waves inside finite-sized structures comprised of different media can benefit from a diakoptics method such as linear embedding via Green's operators (LEGO). Unlike scattering problems, the excitation of EM waves within the bulk dielectric requires introducing sources inside the structure itself. To handle such occurrence, we have expanded the set of LEGO sub-domains - employed to formulate an EM problem - to deal with the inclusion of elementary sources. The corresponding subdomains (bricks) play the role of ``generators'' in the equivalent model. Moreover, if a source is ``turned off'', as it were, the enclosing brick can be utilized as a numerical ``probe'' to sample the EM field. In this paper, we present the integral equations of LEGO modified so as to accommodate generator/probe bricks. Numerical results are provided which demonstrate the validity and the efficiency of the approach

Sensitivity analysis of 3-D composite structures through linear embedding via green's operators

We propose a methodology --- based on linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) --- for solving electromagnetic problems involving large 3-D structures comprised of ND = 1 bodies. In particular, we address the circumstance when the electromagnetic properties or the shape of one body differ from those of the others. In real-life structures such a situation may be either the result of a thoughtful design process or the unwanted outcome of fabrication tolerances. In order to assess the sensitivity of physical observables to localized deviations from the "ideal" structure, we follow a deterministic approach, i.e., we allow for a finite number of different realizations of one of the bodies. Then, for each realization we formulate the problem with LEGO and we employ the EEM to determine the contribution of the ND - 1 "fixed" bodies. Since the latter has to be computed only once, the overall procedure is indeed efficient. As an example of application, we investigate the sensitivity of a 2-layer array of split-ring resonators with respect to the shape and the offset of one element in the array

Iterative solution of field problems with a varying physical parameter

In this paper, linear field problems with a varying physical parameter are solved with the conjugate gradient method and a dedicated extrapolation procedure for generating the initial estimate. The scheme is formulated in detail, and its application to three-dimensional scattering problems for a rectangular conducting plate and an inhomogeneous, dispersive dielectric body are discussed

Accurate full-wave analysis of micromachined coplanar waveguides

We propose a full-wave mode-analysis method suited for micromachined coplanar waveguides (MCPWs). This method is based on the mixed-potential integral equation, in combination with a zero-search algorithm. Results are presented for a semicircular step-index fibre as well as for a MCPW

Computation of finite array effects in the framework of the square kilometer array project

The Square Kilometer Array (SKA) is a very large radio telescope being planned by an international consortium. It would operate in a very broad frequency band and have a collecting area of one square kilometer. In order to achieve a good resolution, this area will be spread over a few tens of stations, located several tens or hundreds of kilometers apart. The Netherlands Foundation for Research in Astronomy (ASTRON) is studying the possibility of covering the mid-range frequencies (~0.2 to 2 GHz) with an instrument based on the phased-array technology. This technology presents the major advantages of avoiding mechanically moving structures and of enabling very flexible beamforming. One of the envisaged broadband antenna elements is the tapered slot antenna, also called Vivaldi antenna. The design of these antennas is based on infinite array models, which automatically include the mutual coupling effects. As each station will probably be made of a very large number of small arrays, it is important to know how these arrays will behave when they are truncated. We developed a computation scheme for arrays of antennas made of metallic fins. We justify the adopted approach, then details are given for the fast resolution of the resulting equation system. Finally, examples are shown for wide dipoles and comments are made about the extension to Vivaldi antenna

A priori error estimate and control in the eigencurrent expansion method applied to linear embedding via Green's operators (LEGO)

Linear embedding via Green's operators (LEGO) [1,2] is a domain decomposition method in which the electromagnetic scattering by an aggregate of Np bodies (immersed in a homogeneous background medium) is tackled by enclosing each object within an arbitrarily-shaped bounded domain T>k (brick), k = 1,... ,Nd (e.g., see Fig. 1). The bricks are characterized electromagnetically by means of scattering operators Skk, which are subsequently combined to form the total inverse scattering operator S_1 of the structure [1]. Finally, we use the eigencurrent expansion method