Cell Curvature and Far-Field Superconvergence in Numerical Solutions of Electromagnetic Integral Equations

Andrew F Peterson

doi:10.1155/2016/9808637

Abstract

Two curved targets are used to explore far-field superconvergence effects arising in numerical solutions of the electric-field and magnetic-field integral equations. Three different orders of basis and testing functions are used to discretize these equations, and three different types of target models (flat facets, quadratic-curved facets, and cubic-curved facets) are employed. Ideal far-field convergence rates are only observed when the model curvature is one degree higher than the basis order.

Highlights

Electromagnetic analysis has often exploited “variational” or “stationary” techniques in an attempt to obtain results that exhibit smaller error or faster convergence than might otherwise be obtained for a given order of approximation
Galerkin method-of-moments (MoM) procedures, which involve the use of identical functions for expanding the unknown surface currents and enforcing the integral equation, sometimes exhibit superconvergence in the far-zone fields or scattering cross section (SCS) [1,2,3,4]
One example of superconvergence arises with the popular Rao-Wilton-Glisson (RWG) solutions of the electric-field integral equation (EFIE) [6], which usually yield SCS error rates of O(h2)O(h3) in practice instead of the O(h) rate expected from basis functions that are only complete to degree 0

Summary

Introduction

Electromagnetic analysis has often exploited “variational” or “stationary” techniques in an attempt to obtain results that exhibit smaller error or faster convergence than might otherwise be obtained for a given order of approximation. Polynomial-complete basis functions seem to produce superconvergent far fields with the MFIE, while mixed-order bases do not. From Warnick’s analysis, the error in the SCS obtained from the EFIE under optimal conditions should converge at a rate of O(h2p+2), where half-integer indices are used for p to denote the mixed-order functions. The SCS error associated with p = 0.0 functions is expected to converge as O(h2), while that of the p = 1.0 functions is expected to converge as O(h4) Note that these rates are one order less than the corresponding rates for the EFIE SCS, based on the extent to which the basis functions are complete to a given degree, but are still superconvergent. This work is intended to build upon and extend the previous work of the author in [7, 11, 15] in establishing baseline convergence rates for numerical solutions of the EFIE and MFIE

Results for Scattering from a Sphere

Results for Scattering from a Torus

Conclusions