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Galerkin implementations of the method of moments (MoM) of the electric-field integral equation (EFIE) have been traditionally carried out with divergence-conforming sets. The normal-continuity constraint across edges gives rise to cumbersome implementations around junctions for composite objects and to less accurate implementations of the combined field integral equation (CFIE) for closed sharp-edged conductors. We present a new MoM-discretization of the EFIE for closed conductors based on the nonconforming monopolar-RWG set, with no continuity across edges. This new approach, which we call "even-surface odd-volumetric monopolar-RWG discretization of the EFIE", makes use of a hierarchical rearrangement of the monopolar-RWG current space in terms of the divergence-conforming RWG set and the new nonconforming "odd monopolar-RWG" set. In the matrix element generation, we carry out a volumetric testing over a set of tetrahedral elements attached to the surface triangulation inside the object in order to make the hyper-singular Kernel contributions numerically manageable. We show for several closed sharp-edged objects that the proposed EFIE-implementation shows improved accuracy with respect to the RWG-discretization and the recently proposed volumetric monopolar-RWG discretization of the EFIE. Also, the new formulation becomes free from the electric-field low-frequency breakdown after rearranging the monopolar-RWG basis functions in terms of the solenoidal, Loop, and the nonsolenoidal, Star and "odd monopolar-RWG", components.Index Terms-Basis functions, electric field integral equation (EFIE), integral equations, moment method.

Abstract-The aim of this paper is to present a study on the potential and limits of the -transform and its inverses. The -transform is an extension of the short-time Fourier transform with characteristics of the wavelet transform. It is mostly used for time-frequency analyses. Two different inverse -transforms have been presented in the literature. We explain why the most recent one is an approximation but a very good one. The level of approximation is calculated in this paper. We then discuss the relative merits of both inverses. A careful study enables us to show that, although both inverses are nearly exact in the infinite continuous domain, this is not true anymore in the practical finite discrete domain. Side effects are quantified, and typical examples are given. Time-frequency filtering is one of the main applications of the -transform. We evaluate the effects that occur when using the -transform and its inverses for filtering.

The multilevel matrix decomposition algorithm (MLMDA) was originally developed by Michielsen and Boag for 2-D TMz scattering problems and later implemented in 3-D by Rius et al. The 3-D MLMDA was particularly efficient and accurate for piece-wise planar objects such as printed antennas. However, for arbitrary 3-D problems it was not as efficient as the multilevel fast multipole algorithm (MLFMA) and the matrix compression error was too large for practical applications. This paper will introduce some improvements in 3-D MLMDA, like new placement of equivalent functions and SVD postcompression. The first is crucial to have a matrix compression error that converges to zero as the compressed matrix size increases. As a result, the new MDA-SVD algorithm is comparable with the MLFMA and the adaptive cross approximation (ACA) in terms of computation time and memory requirements. Remarkably, in high-accuracy computations the MDA-SVD approach obtains a matrix compression error one order of magnitude smaller than ACA or MLFMA in less computation time. Like the ACA, the MDA-SVD algorithm can be implemented on top of an existing MoM code with most commonly used Green's functions, but the MDA-SVD is much more efficient in the analysis of planar or piece-wise planar objects, like printed antennas. Index Terms-Fast integral equation methods, method of moments (MoM), multilayer Green's function, printed antennas.

Abstract-A novel algorithm, the compressed block decomposition (CBD), is presented for highly accelerated direct (noniterative) method of moments (MoM) solution of electromagnetic scattering and radiation problems. The algorithm is based on a block-wise subdivision of the MoM impedance matrix. Impedance matrix subblocks corresponding to distant subregions of the problem geometry are not calculated directly, but approximated in a compressed form. Subsequently, the matrix is decomposed preserving the compression. Examples are presented of typical problems in the range of 5000 to 70 000 unknowns. The total execution time for the largest problem is about 1 h and 20 min for a single excitation vector. The main strength of the method is for problems with multiple excitation vectors (monostatic RCS computations) due to the negligible extra cost for each new excitation. For radiation and scattering problems in free space, the numerical complexity of the algorithm is shown to be 2 and the storage requirements scale with 3 2 . Index Terms-Fast solvers, impedance matrix compression, method of moments (MoM), numerical simulation.

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