On the accuracy of the Adaptive Cross Approximation algorithm

This contribution identifies an often ignored source of uncertainty in the accuracy of the Adaptive Cross Approximation (ACA) algorithm.Postprint (published version

Efficient analysis of sheets with nonzero thickness

The conventional scattering analysis of perfectly conducting plates neglects the scattering contribution of the rim in the discretization of the Electric-Field Integral Equation. This so-called thin-plate scheme manages many less unknowns than the full approach, arising from modelling the whole plate, with acceptable accuracy in many practical applications. A recent approach, so-called thick-plate, has proved to show similar accuracy as the full scheme, also in those cases where the thin-surface fails; namely, the scattering analysis of thick enough plates, especially under oblique incidences, with low grazing angles. In this paper, we reveal how the thick-plate scheme shows improved computational times, especially in large scale computations, as compared to the full approach. Also, we discuss how the thick-plate analysis is amenable to parallelization, thereby leading to computational times comparable with the thin-surface approach.This work was supported by FEDER and the "Spanish Plan Estatal de Investigación Científica y Técnica y de Innovación", under projects: TEC2017-84817-C2-2-R/ AEI/10.13039/501100011033, TEC2016-78028-C3-1-P/AEI/10.1 3039/501100011033, PID2019-107885GB-C31/AEI/10.13039/501100011033 and the Unidad de Excelencia Maria de Maeztu MDM-2016-0600/AEI/10.13039/501100011033, which is financed by the Agencia Estatal de Investigación, Spain, and Catalan Research Group 2017 SGR 219.Peer ReviewedPostprint (author's final draft

Numerical methods for electromagnetic engineering: Class Notes

Full classnotes2022/20231r quadrimestre3.

Tangential-normal surface testing for the nonconforming discretization of the electric-field integral equation

©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 ReviewedPostprint (author's final draft

Novel monopolar MFIE MoM-discretization for the scattering analysis of small objects

We present a novel method of moments (MoM)-magnetic field integral equation (MFIE) discretization that performs closely to the MoM-EFIE in the electromagnetic analysis of moderately small objects. This new MoM-MFIE discretization makes use of a new set of basis functions that we name monopolar Rao-Wilton-Glisson (RWG) and are derived from the RWG basis functions. We show for a wide variety of small objects -curved and sharp-edged-that the new monopolar MoM-MFIE formulation outperforms the conventional MoM-MFIE with RWG basis functions.Peer Reviewe

Integral equation mei applied to three-dimensional arbitrary surfaces

The authors present a new formulation of the integral equation of the measured equation of invariance (MEI) as a confined field integral equation discretised by the method of moments, in which the use of numerically derived testing functions results in an approximately sparse linear system with storage memory requirements and a CPU time for computing the matrix coefficients proportional to the number of unknowns.Peer ReviewedPostprint (published version

GRECO: 30 years of graphical processing techniques for RCS computation

This contribution to the special session in honor of Prof. Rafael Gómez-Martín will address the 30 year development of graphical processing techniques (GRECO) for fast computation of Radar Cross Section (RCS) of electrically large and complex targets. The development of GRECO started in 1988, in the frame of the “Applied research project for the development and validation of numerical methods for RCS prediction, analysis and optimization”, in which I had the pleasure to know Rafael since our groups where participating together in the project. The development of GRECO never stopped, and recently it has been updated by replacing the graphical processing technique for computation of surface reflection and edge diffraction by a hybrid CPU-graphical processing approach. The resulting code has the same accuracy as conventional RCS computation techniques, but detection of shadowed surfaces and edges is one order of magnitude faster than the most efficient O(N logN) implementations.Peer ReviewedPostprint (published version

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

©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 ReviewedPostprint (author's final draft

Nonconforming discretization of the PMCHWT integral equation applied to arbitrarily shaped dielectric objects

©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 ReviewedPostprint (author's final draft

Volumetric testing with wedges for a nonconforming discretization of the PMCHWT formulation

©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 ReviewedPostprint (author's final draft