2013/10/04 by Yassine Boubendir, Boubendir, Yassine, Catalin Turc +1 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1310.1406
openalex publication_date 2013/10/04 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We present several versions of Regularized Combined Field Integral Equation\n(CFIER) formulations for the solution of three dimensional frequency domain\nelectromagnetic scattering problems with Perfectly Electric Conducting (PEC)\nboundary conditions. Just as in the Combined Field Integral Equations (CFIE),\nwe seek the scattered fields in the form of a combined magnetic and electric\ndipole layer potentials that involves a composition of the latter type of\nboundary layers with regularizing operators. The regularizing operators are of\ntwo types: (1) modified versions of electric field integral operators with\ncomplex wavenumbers, and (2) principal symbols of those operators in the sense\nof pseudodifferential operators. We show that the boundary integral operators\nthat enter these CFIER formulations are Fredholm of the second kind, and\ninvertible with bounded inverses in the classical trace spaces of\nelectromagnetic scattering problems. We present a spectral analysis of CFIER\noperators with regularizing operators that have purely imaginary wavenumbers\nfor spherical geometries. Under certain assumptions on the coupling constants\nand the absolute values of the imaginary wavenumbers of the regularizing\noperators, we show that the ensuing CFIER operators are coercive for spherical\ngeometries. These properties allow us to derive wavenumber explicit bounds on\nthe condition numbers of certain CFIER operators that have been proposed in the\nliterature. When regularizing operators with complex wavenumbers with non-zero\nreal parts are used, we show numerical evidence that those complex wavenumbers\ncan be selected in a manner that leads to CFIER formulations whose condition\nnumbers can be bounded independently of frequency for spherical geometries.\n