An Accurate Low-Order Discretization Scheme for the Identity Operator in the Magnetic Field and Combined Field Integral Equations

TL;DR

This paper introduces a novel low-order discretization scheme for the identity operator in magnetic and combined field integral equations, improving accuracy while maintaining solver efficiency and resonance-free properties.

Contribution

It presents a new discretization approach derived from weak-form sources that enhances accuracy of the MFIE without sacrificing convergence or resonance-free characteristics.

Findings

Improved accuracy demonstrated through mesh refinement analysis.

Enhanced near- and far-field scattering results.

CFIE remains interior-resonance free and well-conditioned.

Abstract

A new low-order discretization scheme for the identity operator in the magnetic field integral equation (MFIE) is discussed. Its concept is derived from the weak-form representation of combined sources which are discretized with Rao-Wilton-Glisson (RWG) functions. The resulting MFIE overcomes the accuracy problem of the classical MFIE while it maintains fast iterative solver convergence. The improvement in accuracy is verified with a mesh refinement analysis and with near- and far-field scattering results. Furthermore, simulation results for a combined field integral equation (CFIE) involving the new MFIE show that this CFIE is interior-resonance free and well-conditioned like the classical CFIE, but also accurate as the EFIE.