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©2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., 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., Peer Reviewed, Postprint (author's final draft)

©2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., The monopolar-Rao-Wilton-Glisson (RWG) discretization of the Poggio-Miller-Chan-Harrington-Wu-Tsai (PM-CHWT) integral equation imposes no continuity constraints in the current expansion across the edges arising from the discretization of the boundary surface. The numerical evaluation of the hypersingular kernel contributions can be carried out through the volumetric testing of the fields over a set of tetrahedral elements attached to the boundary surface of the target. This facet-based implementation becomes well-suited for the scattering analysis of composite objects or nonconformal meshes. Furthermore, improved accuracy has been observed in the analysis of moderately small sharp-edged dielectric objects and high contrasts with the proper choice of the height of the testing tetrahedral elements. In this paper, we introduce a novel monopolar-RWG discretization of the PMCHWT formulation where wedge testing elements are adopted. We show with radar cross section results that this scheme offers improved accuracy for a wider range of heights of the testing elements than the approach with tetrahedral testing., Peer Reviewed, Postprint (author's final draft)

The electromagnetic scattering analysis of arbitrarily shaped ferromagnetic bodies is usually carried out with the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) integral equation. In the Method of Moments (MoM) discretization of the PMCHWT formulation, the RWG set is very often adopted in the expansion of the unknown traces of the total electromagnetic fields over the boundary surface of the target. The RWG-schemes are edge-based and become in general well- suited for the analysis of single targets meshed with conformal meshings, where adjacent triangles share common edges. However, their implementation for composite objects becomes elaborate around junctions, where several regions intersect. In this paper, we expand the electric and magnetic field traces over the boundary surface with the monopolar-RWG set, which stands for a facet-based scheme. Unlike the divergence-conforming RWG set, which imposes normal-continuity across edges, the monopolar-RWG set is nonconforming because a fully discontinuous transition across edges is established. This allows for the agile analysis of complex bodies or nonconformal meshes, with nonmatching edges between adjacent triangles. We show the improved RCS-accuracy for the monopolar-RWG discretization of the PMCHWT, with respect to traditional RWG-discretization, for an example of ferromagnetic object., Peer Reviewed, Postprint (published version)

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., Peer Reviewed, Postprint (published version)

©2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., 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., Peer Reviewed, Postprint (author's final draft)

© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., 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., Peer Reviewed, Postprint (author's final draft)

©2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., The Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) integral equation is widely used in the scattering analysis of dielectric bodies. The RWG set is normally adopted to expand the electric and magnetic currents in the Method of Moments (MoM) discretization of the PMCHWT formulation. This set preserves normal continuity across edges in the expansion of currents. However, in the analysis of composite objects, the imposition of such continuity constraint around junctions, where several regions intersect, becomes convoluted. We present a new nonconforming discretization of the PMCHWT formulation so that currents are expanded with no continuity constraint across edges. This becomes well-suited for the analysis of composite objects or nonconformal meshes, where some adjacent facets have no common edges. We show RCS results where the nonconforming PMCHWT implementation, facet-oriented, shows similar or better accuracy as the conventional approach, edge-oriented, for a given degree of meshing., Peer Reviewed, Postprint (author's final draft)

©2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., 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., Peer Reviewed, Postprint (author's final draft)

Recent attention has been devoted to the development of nonconforming implementations of the Electric-Field Integral Equation (EFIE), which impose no continuity constraints in the expansion of the current between adjacent facets. These schemes, based on the facet-oriented monopolar-RWG set, become more versatile than the traditional edge-oriented schemes, based on the RWG set, because they simplify the discretization around junctions in composite objects and because they can handle nonconformal triangulations. The existing nonconforming implementations tackle the numerical evaluation of the inherent hypersingular Kernel contributions of the EFIE by testing the fields over volumetric or surface domains attached to the boundary surface inside the conductor. Hence, the application of such schemes is restricted to closed PeC surfaces. In this paper, we present a novel nonconforming implementation of the EFIE that allows the scattering analysis of open PeC surfaces by testing the fields with a new, 'balancedtangential', strategy. We show for several examples of open PeC surfaces, infinitely long (2D) or arbitrarily shaped (3D), that the proposed scheme provides similar or slightly better accuracy than the RWG-discretization of the EFIE and same meshing., Peer Reviewed, Postprint (published version)

The GNSS rEflectometry, Radio Occultation and Scatterometry onboard the International Space Station (GEROS-ISS) experiment consists of the installation of a GNSS reflectometry (GNSS-R) instrument on the International Space Station (ISS). Due to the complex structure of ISS, the GEROS-ISS instrument suffers from multipath effects. The collected signals are not only from received directly, but also after multiple reflections in the ISS structure. This work analyzes the multipath effect of the GEROS-ISS instrument based on the ISS structure. Using the ray tracing simulation, all rays reaching the instrument after one or two reflections are computed, as well as the corresponding additional delays. This information, together with the direction of arrival to the antenna arrays (up and down-looking), and the co- and cross-polar antenna patterns is used to assess the impact of multipath on the waveforms are demonstrated., Peer Reviewed, Postprint (published version)

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., Peer Reviewed, Postprint (published version)

Traditional method-of-moment implementations of the electric-field integral equation (EFIE) are based on sets of divergence-conforming basis functions, such as the loworder Rao-Wilton-Glisson (RWG) set, which arise from imposing normal continuity in the expanded current across the edges arising from the triangulation around the boundary surface. These schemes are edge-oriented and become well-suited for the analysis of conformal meshings, where pairs of adjacent triangles share common edges. However, they cannot be applied to nonconformal triangulations, arising from the interconnection of independent meshings, for example in the modular modelling of composite objects, because adjacent triangles may not have common matching edges. In this paper, we present several facetoriented implementations of the EFIE that allow the robust and versatile analysis of such objects. Two schemes arise from testing the fields over a set of tetrahedral or wedge elements attached to the boundary surface, inside the conductor. Another scheme, “tangential-normal”, derives from testing the fields over pairs of adjacent triangles such that one triangle matches a particular facet of the surface meshing and the other one is oriented inwards perpendicularly to the surface triangulation., Peer Reviewed, Postprint (published version)

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., Peer Reviewed, Postprint (published version)

The traditional discretizations of the electric-field integral equation (EFIE) impose the continuity of the normal component current across the edges in the meshing. These edgeoriented schemes become awkward in the analysis of composite objects or of closed conductors meshed with nonconformal meshes. In this context, the nonconforming expansion of the current with facet-oriented schemes, like the monopolar-RWG set, with no imposed interelement continuity, leads to EFIEimplementations with enhanced versatility. However, the traditional Galerkin method-of-moment implementation gives rise to hypersingular Kernel contributions, which cannot be evaluated numerically. Recently, we have proposed a nonconforming monopolar-RWG discretization of the EFIE where the testing is carried out over volumetric elements attached to the surface triangulation inside the object under analysis. In this paper, we review the so-called volumetric monopolar-RWG discretization of the EFIE with testing over tetrahedral or wedge elements. These schemes show improved accuracy, when compared with the RWG-discretization, for a particular range of heights of the testing elements. As we show in this paper, this range becomes wider for the wedge testing choice than with the tetrahedral choice., Peer Reviewed, Postprint (published version)

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., Peer Reviewed, Postprint (published version)

Method-of-moment (MoM) implementations of the Electric-field Integral Equation (EFIE) in the scattering analysis of infinitely long (2D) or arbitrarily shaped (3D) conductors have traditionally required, respectively, piecewise-continuous or divergence-conforming basis functions. Recently, nonconforming EFIE-discretizations, with no imposed interelement continuity of current, have been developed by testing the fields over small domains attached to the boundary interfaces, inside the body under analysis. This involves surface or volumetric testing integrals, respectively, for the 2D Transversal-Electric (TE) or 3D MoM-implementations of the EFIE. In this paper, we present new nonconforming discretizations of the EFIE that rely on testing integrals over the boundary interface around the object; namely, line-integrals or surface-integrals, respectively, for the 2D or 3D cases. We show with RCS results that these new, easierto-implement, nonconforming discretizations of the EFIE provide improved accuracy with respect to the traditional conforming, piecewise-linear (2D) or RWG (3D), EFIE-implementations., Peer Reviewed, Postprint (published version)

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., 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., Peer Reviewed, Postprint (author's final draft)

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., Peer Reviewed, Postprint (published version)