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

Abstract

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.Index Terms-Basis functions, electric field integral equation (EFIE), integral equations, moment method.

A Moment-Based Study on the Impedance Effect of Mutual Coupling for VLF Umbrella Antenna Arrays

“…The current I(s) along the wire satisfies the following electric field integral equation (EFIE) [4,[26][27][28][29]:…”

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

“…The monopolar-RWG space of current can be decomposed into two edge-oriented subspaces of current, such that the basis functions are defined in terms of the type of transition of the normal component of the current across edges [4] …”

“…The resulting numerical implementations are little demanding in computational terms because the hypersingular Kernel contributions are cancelled out [2]. Recently, nonconforming schemes based on the facet-oriented monopolar-RWG set [3], with no interelement continuity constraint, have been developed for the discretization of the EFIE in the EM scattering analysis of closed conductors [4] [5]. These implementations carry out the numerical evaluation of the hypersingular Kernel contributions by testing the fields over volumetric subdomains inside the body, tetrahedral elements [4] or wedges [5], attached to the surface triangulation.…”

“…Recently, nonconforming schemes based on the facet-oriented monopolar-RWG set [3], with no interelement continuity constraint, have been developed for the discretization of the EFIE in the EM scattering analysis of closed conductors [4] [5]. These implementations carry out the numerical evaluation of the hypersingular Kernel contributions by testing the fields over volumetric subdomains inside the body, tetrahedral elements [4] or wedges [5], attached to the surface triangulation. However, the generation of the impedance matrix elements becomes rather elaborate and more time-consuming than the conventional surface-tested Galerkin RWG-discretization.…”

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

“…However, generating conformal discretizations for engineering system-level simulations is far from trivial, as the complexity of modern engineering applications increases at a fast pace. Among the previous works addressing the above mentioned deficiencies, we mention recent works [28][29][30][31][32].…”