Ivan Sekulic

Volumetric Testing Parallel to the Boundary Surface for a Nonconforming Discretization of the Electric-Field Integral Equation

The volumetric monopolar-RWG discretization of the electric-field integral equation (EFIE) imposes no continuity constraint across edges in the surface discretization around a closed conductor. The current is expanded with the monopolar-RWG set and the electric field is tested over a set of tetrahedral elements attached to the boundary surface. This scheme is facet-oriented and therefore, well suited for the scattering analysis of nonconformal meshes or composite objects. The observed accuracy, though, is only competitive with respect to the RWG-discretization for a restricted range of heights of the tetrahedral elements. In this communication, we introduce a novel implementation of the volumetric monopolar-RWG discretization of the EFIE with testing over a set of wedges. We show with RCS and near-field results that this scheme offers improved accuracy for a wider range of heights than the approach with tetrahedral testing. The application of the wedge testing to the even-surface odd-volumetric monopolar-RWG discretization of the EFIE, edge-oriented and therefore less versatile, shows similar accuracy as with tetrahedral testing, which is a sign of robustness.

Tangential-Normal Surface Testing for the Nonconforming Discretization of the Electric-Field Integral Equation

Nonconforming implementations of the electric-field integral equation (EFIE), based on the facet-oriented monopolar-RWG set, impose no continuity constraints in the expansion of the current between adjacent facets. These schemes become more versatile than the traditional edge-oriented schemes, based on the RWG set, because they simplify the management of junctions in composite objects and allow the analysis of nonconformal triangulations. Moreover, for closed moderately small conductors with edges and corners, they show improved accuracy with respect to the conventional RWG-discretization. However, they lead to elaborate numerical schemes because the fields are tested inside the body, near the boundary surface, over volumetric subdomains attached to the surface meshing. In this letter, we present a new nonconforming discretization of the EFIE that results from testing with RWG functions over pairs of triangles such that one triangle matches one facet of the surface triangulation and the other one is oriented perpendicularly, inside the body. This “tangential-normal” testing scheme, based on surface integrals, simplifies considerably the matrix generation when compared to the volumetrically tested approaches.

GEROS-ISS, a demonstration mission of GNSS remote sensing capabilities to derive geophysical parameters of the earth surfaces: Altimetry performance evaluation

The GNSS rEflectometry, Radio Occultation and Scatterometry onboard International Space Station (GEROS-ISS) is an innovative experiment for climate research, proposed in 2011 within a call of the European Space Agency (ESA) for installation at the ISS. This international proposal was the only one selected for further studies by ESA out of ~25 submitted ones. In this work, the assessment of the instrument performance for the near-nadir altimetry (GNSS-R) mode is assessed, including the effects of multi-path in the ISS structure, the electromagnetic-bias, and the orbital height decay. In the absence of ionospheric scintillations, the altimetry rms error is <; 50 cm for a swath <; ~250 km and for U10 <; 10 m/s. If the transmitted power is 3 dB higher (likely to happen at beginning of life of the spacecraft), mission requirements (rms error is <; 50 cm) are met for all ISS heights and U10 up to 15 m/s. However, around 1.5 GHz, the ionosphere can induce significant fading, from 2 to > 20 dB at equatorial regions, mainly after sunset, which will seriously degrade the altimetry and the scatterometry performances of the instrument.

Tangential-normal line testing for a nonconforming discretization of the transversal-electric Electric-Field Integral Equation for 2D conductors

The Method-of-Moment (MoM) discretization of the Electric-Field Integral Equation (EFIE) for a transversal electric (TE) illuminating plane wave impinging on an infinitely long cylinder (2D-object) traditionally requires continuous piecewise linear basis functions. These basis functions are particularly convenient in the numerical implementation because they reduce the degree of the Kernel singularity. Recently, a nonconforming implementation of the TE-EFIE discretized with discontinuous piecewise linear basis functions has been successfully developed with the testing procedure done over small surface entities attached to the boundary of the object, inside the body under analysis. In this paper we present a novel nonconforming discretization of the TE-EFIE based on discontinuous piecewise linear basis functions with a testing procedure that relies only on line integrals. This allows for an easier and more efficient computation of the impedance matrix elements while preserving the improved far-field accuracy observed for sharp edged objects in the previous surface-tested TE-EFIE implementation.

Regularization of the 2D TE-EFIE for homogeneous objects discretized by the Method of Moments with discontinuous basis functions

The discretization of the Electric-Field Integral Equation (EFIE) by the Method of Moments (MoM) for a transversal electric (TE) illuminating wave impinging on an infinitely long cylinder (2D-object) is traditionally carried out with continuous piecewise linear basis functions. In this paper, we present a novel discretization of the TE-EFIE formulation for the scattering analysis of homogeneous, perfectly conducting 2D-objects based on the expansion of the currents around the line-boundary through discontinuous piecewise linear or piecewise constant basis functions. We show for several infinitely long cylinders, with smooth or sharp-edged sections, the good accuracy of the proposed approach in the computation of far-field and near-field quantities, such as RCS and currents, with respect to the observed accuracy in conventional continuous piecewise linear discretizations.

Versatile and Accurate Schemes of Discretization in the Scattering Analysis of 2-D Composite Objects With Penetrable or Perfectly Conducting Regions

The method-of-moment discretization of boundary integral equations in the scattering analysis of closed infinitely long (2-D) objects, perfectly conducting (PEC) or penetrable, is traditionally carried out with continuous piecewise linear basis functions, which embrace pairs of adjacent segments. This is numerically advantageous because the discretization of the transversal component of the scattered fields, electric (TE) or magnetic (TM), becomes free from hypersingular Kernel contributions. In the analysis of composite objects, though, the imposition of the continuity requirement around junction nodes, where the boundaries of several regions intersect, becomes especially awkward. In this paper, we present, for the scattering analysis of composite objects, a new combined discretization of the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) integral equation, for homogeneous dielectric regions, and the electric-field integral equation, for PEC regions, such that the basis functions are defined strictly on each segment, with no continuity constraint between adjacent segments. We show the improved observed accuracy with the proposed TE-PMCHWT implementation on several dielectric objects with sharp edges and corners and moderate or high contrasts. Furthermore, we illustrate the versatility of these schemes in the analysis of 2-D composite piecewise homogeneous objects without sacrificing accuracy with respect to the conventional implementations.

GNSS-R altimetry performance analysis for the GEROS experiment on board the international space station

The GEROS-ISS (GNSS rEflectometry, Radio Occultation and Scatterometry onboard International Space Station) is an innovative experiment for climate research, proposed in 2011 within a call of the European Space Agency (ESA). This proposal was the only one selected for further studies by ESA out of ~25 ones that were submitted. In this work, the instrument performance for the near-nadir altimetry (GNSS-R) mode is assessed, including the effects of multi-path in the ISS structure, the electromagnetic-bias, and the orbital height decay. In the absence of ionospheric scintillations, the altimetry rms error is <50 cm for a swath <~250 km and for U10 <10 m/s. If the transmitted power is 3 dB higher (likely to happen at beginning of life of the GNSS spacecrafts), mission requirements (rms error is <50 cm) are met for all ISS heights and for U10 up to 15 m/s. However, around 1.5 GHz, the ionosphere can induce significant fading, from 2 to >20 dB at equatorial regions, mainly after sunset, which will seriously degrade the altimetry and the scatterometry performances of the instrument.

Improved accuracy in the scattering analysis of infinitely long ferromagnetic objects

The scattering of transversal magnetic (TM) electromagnetic waves impinging on infinitely long homogeneous ferromagnetic objects is usually analyzed with the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) integral equation. The Method-of-Moments (MoM) discretization of TM-PMCHWT usually requires continuous piecewise linear basis functions. These basis functions are especially well suited in the analysis of single radar targets since they cancel out the hypersingular terms in the scattered magnetic field. However, the analysis of complex objects, with junctions or nonmatching segmentations, becomes particularly inconvenient because of the interelement continuity constraints. In this work, in order to provide enhanced versatility, we propose the discretization of the currents with discontinuous piecewise linear basis functions. Since the hypersingular Kernel contributions cannot be evaluated through a conventional Galerkin testing scheme, we propose two new testing procedures. We show the improved RCS-accuracy for this nonconforming discretization of TM-PMCHWT, with respect to traditional continuous piecewise linear discretization, for an example of infinitely long sharp-edged ferromagnetic cylinder.

Versatile and accurate schemes of discretization for the electromagnetic scattering analysis of arbitrarily shaped piecewise homogeneous objects

Abstract The discretization by the method of moments (MoM) of integral equations in the electromagnetic scattering analysis most often relies on divergence-conforming basis functions, such as the Rao–Wilton–Glisson (RWG) set, which preserve the normal continuity of the expanded currents across the edges arising from the discretization of the target boundary. Although for such schemes the boundary integrals become free from hypersingular kernel-contributions, which is numerically advantageous, their practical implementation in real-life scenarios becomes particularly cumbersome. Indeed, the application of the normal continuity condition on composite objects becomes elaborate and convoluted at junction-edges, where several regions intersect. Also, such edge-based schemes cannot even be applied to nonconformal meshes, where adjacent facets may not share single matching edges. In this paper, we present nonconforming schemes of discretization for the scattering analysis of complex objects based on the expansion of the boundary unknowns, electric or magnetic currents, with the facet-based monopolar-RWG set. We show with examples how these schemes exhibit great flexibility when handling composite piecewise homogeneous objects with junctions or targets modeled with nonconformal meshes. Furthermore, these schemes offer improved near- and far-field accuracy in the scattering analysis of electrically small single sharp-edged dielectric targets with moderate or high dielectric contrasts.

Hierarchical discretization of the PMCHWT formulation with jump current discontinuities for the scattering analysis of ferromagnetic objects

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.