Showing papers by "George A. Kyriacou published in 2004"

A Modified Perturbation Method for Three-dimensional Time Harmonic Impedance Tomography

Abstract: A reconstruction algorithm for three dimensional time harmonic impedance imaging based on the Modified Perturbation Method (MPM), [1], is proposed. Both the object conductivity (σ) and permittivity (e) are reconstructed. The original Perturbation method developed for static problems was modified in order to apply in time harmonic problem in higher frequency. In this case complex permittivity and complex voltages are involved. So, major modifications have been made in order to achieve accepted results. The jacobian matrix is expressed in complex form and the modified perturbation reconstruction algorithm formulated accordingly. A number of successful reconstructions were carried out for different complex permittivity profiles, but all of them based on a computer phantom approach.

A 2-D Finite Difference Frequency Domain (FDFD) Eigenvalue Method for Orthogonal Curvilinear Coordinates.

Abstract: A 2-D FDFD eigenvalue method in orthogonal curvilinear coordinates is presented in this paper. It is based on the combination of Finite Difference Frequency Domain method in two dimensions with

Mode matching analysis of multiple offset coaxial irises in circular waveguide

Abstract: The step junction between a circular and an eccentric coaxial waveguide is analysed using a rigorous mode matching technique along with the Graff’s addition theorem for cylindrical functions. The necessary expressions including the coupling integrals are considered analytically. Based on this analysis the off-centred coaxial iris in a circular waveguide is studied. Its properties are pointed out and the single and dual irises on the same diaphragm features are exploited for the design of bandpass filters.

Horn Antennas Analysis Using a Hybrid Mode Matching-Auxiliary Sources Technique

Abstract: A Hybrid technique for the analysis of pyramidal horn antennas is proposed in this paper. The transition from a relatively small feeding waveguide to a larger radiating aperture is analyzed using the mode matching technique, while the discontinuity between the horn and free space is analyzed using the method of auxiliary sources. The resulting procedure is very stable and accurate while the computational time is quite small since all the coupling integrals involved in the mode matching are evaluated analytically. I. Introduction The proposed hybrid method aims at the accurate prediction of the return loss and the radiation pattern of horn antennas. Approximate methods used in the past for the analysis of this type of antennas failed to accurately calculate the VSWR as well as the far-out sidelobes and backlobe radiation patterns. A hybrid method was proposed in [1] for the analysis of conical horn antennas, where the Mode Matching Technique (MMT) was used for the evaluation of the scattering parameters of the antenna and the method of moments for the analysis of the transition between the horn and the free space. This method, restricted to circularly symmetric structures, proved to be very accurate. Liu et al [2], proposed a similar technique for the analysis of rectangular horn antennas. In the proposed paper the horn antenna is divided into a series of waveguide sections and step junctions, which are analyzed using a closed-form MMT developed in our previous work [3]. In this manner the field within the horn as well as on its aperture can be described by the MMT. In [3] we assumed that the aperture was a perfect termination for all the incident waveguide modes. This approximation causes inaccuracies, especially in the antenna input impedance and when the aperture electrical dimensions are relatively small (in terms of wavelengths). In order to overcome this shortcome this paper aims at the characterization of the aperture discontinuity as an imperfect junction between the horn and the free space. The resulting hybrid technique can accurately and efficiently evaluate the return loss and the radiation characteristics of the antenna under investigation. This is due to the closed form representation of the coupling integrals involved in the MMT, while the key feature of the MAS is the displacement of the location of the auxiliary sources with respect to the actual boundary. This last feature provides a non-vanishing distance between sources and observation points, leading to a stable numerical code. Moreover, this procedure is applicable to any waveguide or horn geometries, but it could also be applied to other structure like the leaky waveguides.

Authors' Reply to “Comment on ‘A FEM Analysis of Open Boundary Structures Using Edge Elements and a Cylindrical Harmonics Expansion’”

Abstract: The exact theoretical harmonics expansion for open boundary structures is obviously the one presented by Jin (2004). This is actually the expansion that was used at the beginning of our effort related to our original article (Allilomes et al., 2004). The difficulties referred to in Jin (2004), concerning the formulation and the numerical solution of the eigenvalue problem, were encountered from the first steps. In turn it was decided to solve the problem for the eigenvalue spectrum around ( β ko )2 1 as a first-order approximation, namely,

Comments on “A FEM Analysis of Open Boundary Structures Using Edge Elements and a Cylindrical Harmonics Expansion”

Abstract: where kρ = √ k2 o − β2. Using the above correct expressions, one can still carry out the finite element analysis. However, the final matrix equation cannot be cast into the form of a generalized eigenvalue problem that can be solved for β. Instead, the matrix is related to β in a much more complex form and a root searching method to solve for β is usually very time consuming. That is precisely the reason why the finite element method combined with harmonics expansion has not been effective for open dielectric-waveguide problems, although the method has been used for deterministic (scattering and radiation) problems for nearly 30 years. In the latter, kρ is known. The same holds true for the combined finite element and boundary integral method.

An Eigenvalue Hybrid FEM Formulation for 2D Open Structures Using Mixed type Node/Edge Elements and a Cylindrical Harmonics Expansion

Abstract: A Finite element formulation for the solution of the two-dimensional eigenvalue problem for open radiating structures is proposed. The semi-infinite solution domain that occurs in such problem is modelled using an expansion in an infinite sum of cylindrical harmonics, while the structure itself is described by the finite element method. The two mathematical models are coupled by exploiting the tangential field continuity condition. In fact for the truncation of the finite element mesh a fictitious cylindrical domain boundary is used which encloses the opening of our structure. On that fictitious boundary we impose the field continuity condition formulating in that way a generalized eigenvalue problem taking in to account Sommerfeld radiation condition. This final eigenvalue problem is solved using the Arnoldi subspace iterative technique, [5]. I. Introduction The finite element method has proven its robustness in almost all the forms of closed boundary problem. But when it comes to open radiating structures which means that the solution domain extends to infinity, this method cannot be imposed directly. In such cases several extensions of the method have been proposed. The idea behind all these extensions is the implementation of artificial boundaries enclosing the structures, which are transparent to the field solution. This enables the conversion of the unbounded problem to its bounded equivalent. The main representatives of this approach are techniques like the Absorbing Boundary Conditions and the Perfect Matching Layer. Another way to cope with open boundary problems is by considering a field solution satisfying the radiation condition, for the semi-infinite domain beyond the artificial boundary. In turn, this solution is combined with the Finite Element formulation by employing the Field continuity conditions on the artificial boundary. This basic idea had led to a variety of Hybrid methods like the Unimoment [1], and the By-moment method, [2]. In the present effort we proposed a FEM eigenvalue formulation for two-dimensional (2D) open radiating structures similar to the unimoment method. The 2-D solution domain in the generalized case is enclosed by a fictitious circular contour (C). But, for certain shapes of the guiding structures, it is also possible to enclose only the radiating aperture of the structure in an angular sectorC’. For the field solution inside-C the FEM formulation is applied based on a triangular mixed node/edge elements discretization. Thus being able to model arbitrary shaped radiating 2D structures. The field solution in the semi-infinite space outside-C is expressed by an expansion in an infinite series of cylindrical harmonics. The final formulation is obtained by imposing the field continuity conditions on the fictitious surface and exploiting the orthogonality properties of the cylindrical harmonics. The proposed technique preserves the sparsity of the matrix, and the elemental matrices of the final formulation are evaluated analytically. The present work is based on our recent publication,[3], where rectangular mixed node/edge elements were employed. The disadvantage of [3] is the poor discretization of the solution domain, which especially along the circular contour-C causes undesired stair-case effects. Thus the main enhancements of the present approach are the analytical evaluation of the elemental matrices and the use of triangular elements. The use of triangular elements, enables us to discretize accurately the fictitious circular boundary as well as the analytical evaluation of the contour integrals along that.