On the use of combined surface integral equations for the analysis of high contrast penetrable objects

• Published in: IET microwaves, antennas & propagation Vol. 17; no. 4; pp. 301 - 312
• Main Authors: Nazari, Moein, Moini, Rouzbeh, Fortin, Simon, Dawalibi, Farid P.
• Format: Journal Article
• Language: English
• Published: Wiley 01.03.2023
• Subjects: computational electromagnetics; dielectric resonators; integral equations; method of moments; scattering
• ISSN: 1751-8725; 1751-8733
• DOI: 10.1049/mia2.12340

Accurate solutions of electromagnetic scattering problems involving objects made of materials with large permittivity contrasts are considered. Problems are formulated with different commonly used combined surface integral equations (SIEs). All studied formulations are discretised through the method of moments with rooftop basis functions over flat quadrilaterals represented as bilinear surfaces, with razor‐blade functions being used for the testing procedure. The accuracy of the results is first investigated in detail for several frequencies and permittivity values using different numerical measures. It is shown that numerical instabilities may appear at frequencies corresponding to the physical resonances of the object, in particular in the near field and for large material parameter contrasts. The example of a dielectric resonator (DR) with cubic geometry is considered for the purpose of analysis, especially since to achieve smaller DR type antennas, it is necessary to use higher contrast materials. The accuracy of the combined surface integral equations to determine the natural resonant modes of the DR is investigated. It is found that the resonance modes can be accurately determined by exploring the radar cross section (RCS) of the DR in free space only if a proper combination of the electric and magnetic fields equations is applied. The modal analysis of rectangular dielectric resonators are addressed using different combined surface integral equations (T‐Muller, N‐Muller, PMCHWT, and TENENH). All developed formulations are discretised through the method of moments with rooftop basis functions over flat quadrilaterals represented as bilinear surfaces, with razor‐blade functions being used for the testing procedure.