Delet

The issue of transforming the first-kind, singular EFIE into a second-kind regular equation is addressed for a general printed structure via a novel approach, with separation of the integral operator in two parts, and numerically based inversion of their singular parts. The improvements introduced by this procedure are described, along with the insight given into the practical convergence of the EFIE; this appears as a consequence of the singularity of the kernel, to be properly retained and handled in the solution process.

We describe a novel basis of hierarchical, multiscale functions that are linear combinations of standard Rao-Wilton-Glisson (RWG) functions. When the basis is used for discretizing the electric field integral equation (EFIE) for PEC objects it gives rise to a linear system immune from low-frequency breakdown, and well conditioned for dense meshes. The proposed scheme can be applied to any mesh with triangular facets, and therefore it can be used as if it were an algebraic preconditioner. The properties of the new system are confirmed by numerical results that show fast convergence rates of iterative solvers, significantly better than those for the loop-tree basis. As a byproduct of the basis generation, a generalization of the RWG functions to nonsimplex cells is introduced.

We present a synthesis of the sparse matrix/adaptive integral method (SM/AIM) and the multiresolution (MR) approach for the analysis of electrically large finite arrays, with planar or 3-D radiating elements; the two methods were separately introduced previously. The use of the MR has the effect of a preconditioner and speeds up the convergence rate of the SM/AIM of almost two orders of magnitude, with a total reduction of the numerical complexity with respect to the standard MoM of almost three orders of magnitude.

In this paper, a technique is presented for the accurate analysis of large and/or complex arrays with limited numerical effort is presented. The method combines the Synthetic basis Function eXpansion (SFX) approach and the Dual-IsoScalar Multi-Resolution (DIS-MR) approach. The SFX generates few global basis functions on portions of the array, and uses them as basis functions in the array analysis; the DIS-MR approach manages to generate "wavelet-like" hierarchical multiscale vector functions for any meshed geometry, and well controls the MoM condition number. Their combination naturally extends SFX to a multigrid scheme.

In this work we present a new Multi-Resolution (MR) basis for the analysis of a generic 3D conductor via the EFIE-MoM. The (possibly curved) conductor is discretized with (planar) triangular cells, and the MR basis is constructed as a linear combination of the Rao-Wilton-Glisson (RWG) functions defined on the mesh.

Large, finite arrays are often studied in hypothesis of infinite structure, thus allowing the reduction of the numerical effort to that of a single periodic cell. Sometimes this approximation leads to reasonable results in predicting the input impedance of elements far out from the edges. However, for near edge elements it is visibly wrong. Furthermore, when wide beam angle scanning occurs, the effects of truncation can be relevant also for elements very far from the edges. A truncated Floquet waves (TFW) method has been presented, for predicting the distributions of the radiating currents, including those belonging to the edge elements of the array, while retaining a number of unknowns which is comparable with that occurring for the infinite array problem. This approach is based on the method of moments (MoM) solution of an integral equation in which the unknown function can be interpreted as due to the edge diffracted field excited by the Floquet waves of the infinite structure. In this paper, the formulation of the TFW method is applied to the 3D case of rectangular array of slots in an infinite ground-plane.

This second part of a two-paper sequence deals with the generalization to three-dimensional (3-D) arrays of the truncated Floquet wave (TFW) diffraction method for the full wave analysis of large arrays. This generalization potentially includes arrays consisting of microstrip excited slots, cavity-backed apertures, and patches. The formulation is carried out first by deriving an appropriate fringe integral equation (IE) and next by defining entire domain basis functions in terms of global-array functions shaped as TFW diffracted rays whose analytical expression is derived on the basis of prototype canonical problems. The efficiency and the accuracy of this method is demonstrated by comparison with the results of an element-by-element full wave approach for a rectangular slot array.

This second part of a two-paper sequence deals with the generalization to three-dimensional (3-D) arrays of the truncated Floquet wave (TFW) diffraction method for the full wave analysis of large arrays. This generalization potentially includes arrays consisting of microstrip excited slots, cavity-backed apertures, and patches. The formulation is carried out first by deriving an appropriate fringe integral equation (IE) and next by defining entire domain basis functions in terms of global-array functions shaped as TFW diffracted rays whose analytical expression is derived on the basis of prototype canonical problems. The efficiency and the accuracy of this method is demonstrated by comparison with the results of an element-by-element full wave approach for a rectangular slot array.

This paper deals with a multiresolution approach to the finite-element solution of the Electric Field Integral Equation (EF IE) formulation of the boundary value problem for Maxwell equations. After defining a multiresolution set of discretized spaces, each of them is first separated into solenoidal and non-solenoidal complementary spaces. The possibility of obtaining these two spaces with a scalar-to-vector space mappings is used to consider first two separate scalar wavelet decompositions, and then to transform them properly into the two desired vector finite element sets, finally joined to obtain the complete multiresolution basis. Numerical results, obtained for real life antennas, are presented to verify the actual sparsity of the system matrix and to show the fast convergence behaviour of iterative solvers.