Eduard Ubeda

The scattering analysis of perfectly conducting plates, with very small electrical thickness, in the free space is normally carried out through the zero-thickness approximation, which arises from modelling the whole closed surface enclosing the plate as an open surface. The resulting accuracy, though acceptable in many practical applications, deteriorates drastically for growing plate thicknesses or under grazing-angle incidence. In this paper, we provide a thorough description of the recently proposed thick-plate approach, which, while maintaining the agile single-mesh management of the zero-thickness scheme, offers improved accuracy with restricted computational overhead for a wider range of plate thicknesses or plane wave incidences. The computed thick-plate RCS solution deviation as compared with the zero-thickness and full method-of-moment solutions is quantified for an illustrative variety of flat perfectly conducting structures with different electrical dimensions, shapes (rectangular or circular), rim contour (straight or rounded) and plane wave incidence (perpendicular or grazing).

In this work, we propose a method to enhance the convergence of the Born series. The Born series is widely used in scattering theory, but its convergence is only guaranteed under certain restrictive conditions that limit the cases where this formulation can be applied. The proposed method, based on modifying the singularities of the resolvent operator by a change of variables, accelerates the convergence of the series or even achieves convergence in otherwise divergent cases. Due to its low computational cost and ease of implementation, the method preserves the advantages of the Born series, while it extends its range of applications. It can also be applied to a variety of methods relying on the same mathematical principles as the Born series. Numerical examples are provided to show that a significant improvement can be achieved with simple techniques and with limited knowledge about the operator spectrum.

The accuracy of the Adaptive Cross Approximation (ACA) algorithm, a popular method for the compression of low rank matrix blocks in Method of Moment computations, is sometimes seriously compromised by unpredictable errors in the convergence criterion. This paper proposes an alternative criterion, based on global sampling of the error in the elements of the ACA compressed matrix. The sampling error depends on the size of the sample but also on the population distribution of the error, which makes it difficult to control the error independently of the underlying problem. However, as argued and demonstrated in the paper, the distribution of the error converges to the same unique probability distribution function for all low rank matrices. Complementing the sampling criterion with a simple mechanism to detect this convergence, we arrive at a criterion that controls the error irrespective of the underlying problem. As a practical example the RCS of a moderate size metallic ogive is computed to illustrate the merits of the proposed criterion. The proposed algorithm may also be useful in other methods that approximate low-rank matrices by interpolation of a reduced set of its elements.

The surface integral equation (SIE) method, discretized with the method of moments, is a well-established methodology for the scattering analysis of subwavelength plasmonic nanoparticles. SIEs are usually discretized with low-order basis functions that preserve the normal continuity of the surface currents across the edges arising in the meshed boundary, such as Rao-Wilton-Glisson (RWG) functions. However, the plasmonic enhancement modeling on sharp-edged particles is an extremely challenging task, especially due to the singular fields exerted at sharp corners, exposing a slow (or no) convergence in the computation of the scattering and absorption spectra. In this paper, we propose an alternative discretization strategy based on a discontinuous basis function set in conjunction with a volumetric-tetrahedral testing scheme. We demonstrate the potential of the proposed discretization scheme by studying scattering and absorption spectra of three canonical plasmonic polyhedra, i.e., a hexahedral, an octahedral, and a tetrahedral silver inclusion. The results expose an improved accuracy and faster convergence in both far-field and near-field regions when compared to the standard RWG implementation. The proposed discretization scheme can offer faster and more accurate routes towards the exploration and design of the plasmonic resonant spectrum of sharp-edged nanoparticles and nanoantennas.

The Poggio-Miller-Chan-Harrington-Wu-Tsai (PM-CHWT) integral equation discretized with the method of moments (MoM) in conjunction with the edge-based Rao-Wilton-Glisson (RWG) set is normally used in the electromagnetic scattering analysis of arbitrarily shaped penetrable structures. However, since the RWG basis functions impose the normal-current continuity across adjacent triangles arising in the surface mesh, the RWG-based implementations are only valid for conformal triangulations. In this paper, we introduce a nonconforming PMCHWT domain decomposition method for the scattering analysis of penetrable structures which is valid for conformal and nonconformal meshes. This scheme does not require the definition of artificial enclosing surfaces and auxiliary currents in the process of tearing the original domain. The transition of the electric and magnetic currents across adjacent sub-domains is imposed with the facet-based monopolar-RWG set together with a volumetric testing scheme over the tearing contour. The proposed method allows for the construction of an effective block-diagonal preconditioner for large and multi-scale problems.

In recent years, there has been a growing interest in developing invisibility cloaks that can conceal an object. These techniques are often based either on coating a dielectric or conducting object with a homogeneous plasmonic layer of negative permittivity [1] or on creating multilayer structure [2] that cancels the scattering of the cloaked object (i.e., scattering cancelation technique). The technique may also be based on an inhomogeneous layer that bends electromagnetic waves around the region occupied by the cloaked object without interacting with it (i.e., transformation optics technique) [3].

In the discretization of the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) formulation by the Method of Moments (MoM), the unknown currents are usually expanded with the divergence-conforming RWG set. Recently, the discretization of the PMCHWT formulation with the monopolar-RWG basis functions, discontinuous across edges, has been successfully developed through a volumetric-tetrahedral testing scheme. We present a novel even-surface odd-volumetric monopolar-RWG PMCHWT-discretization that relies on the rearrangement of the monopolar-RWG set in terms of the RWG and the odd-monopolar-RWG subsets. This scheme offers improved accuracy for a wider range of heights of the testing tetrahedral elements than the volumetrically tested monopolar-RWG PMCHWT-discretization in the analysis of small sharp-edged ferromagnetic targets.

This contribution identifies an often ignored source of uncertainty in the accuracy of the adaptive cross approximation algorithm, and proposes a combination of adaptations that reduce this uncertainty with negligible additional computational cost.