A High Order Numerical Investigation of Electromagnetic Scattering From a Torus and a Circular Loop

Abstract

The normally integrated magnetic field integral equation (NIMFIE) formulation is used to generate accurate numerical results for toroidal scatterers. Numerical data for the surface currents and scattering cross section induced by a plane wave on a perfectly conducting torus are presented. The special case of a thin circular loop is also examined. These results are expected to find use in numerical validation.Index Terms-Electromagnetic scattering, integral equations, numerical analysis, software verification and validation.

Low‐frequency electromagnetic scattering by a metal torus in a lossless medium with magnetic dipolar illumination

“…Taking into account the harmonic functions (2), we initially solve independently the boundary value problems (23) and (26), to obtain H s 0 and H s 3 , respectively and then proceed to the more complicated problems (24) and (25), to calculate H s 2 (thus E s 1 / and E s 3 . The appropriate non-penetrable boundary conditions for the total electromagnetic fields on the surface D s of the metallic object given by (28) and followed by the radiation conditions (30) fit the aforementioned boundary value problems.…”

“…The simplest treatment concern field H s 3 , since the primary field (14), that is, H i 3 , is constant. Here, we have to solve the potential boundary value problem (26), accompanied by (22), with the Neumann boundary condition (28) on S for n D 3, which in terms of O n given by (36) is as follows:…”

Progress in controlled accuracy numerical solutions of integral equations

“…Developments in high order (polynomial) basis functions are fairly mature [1][2][3], and these have been demonstrated to produce high accuracy for a variety of smooth targets [4][5][6][7]. Despite the widespread use of flat-faceted models, smooth targets will require curved-patch models for accuracy [1,6].…”

“…In the authors' previous work [4][5]7] polynomial expansion functions of degree p and order q = p + 1 produced numerical results that exhibited residual errors that decreased as integer powers of cell size h, for small cell sizes. For the 3D electric-field integral equation (EFIE), the electric field residual decreased as O(h q-1 ), while for the magnetic field integral equation (MFIE), the magnetic field residual decreased as O(h q ).…”

“…Smooth three-dimensional problems such as spheres and toroids have been treated to high accuracy with polynomial representations [7]. However, most practical 3D structures contain edges or corners.…”