Nonconforming Discretization of the Electric-Field Integral Equation for Closed Perfectly Conducting Objects

• Published in: IEEE transactions on antennas and propagation 2014-08, Vol.62 (8), p.4171-4186
• Main Authors: Ubeda, Eduard, Rius, Juan M., Heldring, Alex
• Format: Article
• Language: English
• Subjects: Antennas; Applied classical electromagnetism; Basis functions; Bodies; Conductors; Continuity; Dielectric objects; Discretization; electric field integral equation (EFIE); Electrical junctions; Electromagnetic scattering; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; Electromagnetism; electron and ion optics; Electromagnetisme; Enginyeria de la telecomunicació; Equacions diferencials i integrals; Equacions integrals; Exact sciences and technology; Frequencies; Fundamental areas of phenomenology (including applications); Galerkin methods; Impedance; Integral equations; Junctions; Matemàtiques i estadística; Mathematical models; Method of moments; MFIE; moment method; Moments; Physics; Surface impedance; Testing; Vectors; Àrees temàtiques de la UPC
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2014.2325954

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.