Robust integral formulations for electromagnetic scattering from three-dimensional cavities

Abstract

Scattering from large, open cavity structures is of importance in a variety of electromagnetic applications. In this paper, we propose a new well conditioned integral equation for scattering from general open cavities embedded in an infinite, perfectly conducting half-space. The integral representation permits the stable evaluation of both the electric and magnetic field, even in the lowfrequency regime, using the continuity equation in a post-processing step. We establish existence and uniqueness results, and demonstrate the performance of the scheme in the cavity-of-revolution case. High-order accuracy is obtained using a Nyström discretization with generalized Gaussian quadratures.

An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects

“…There are no known numerically useful closed-form expressions for g i m . The evaluation of these functions occupies a significant portion of the run-time of the resulting solver [43] (approximately 50%, as shown in Table 1), and therefore an efficient scheme for computing them is important. Expansions of these functions in terms of halforder Hankel functions have, as of yet, proven to be somewhat expensive to evaluate [15], and designing robust contour integration methods for large values of m is quite complicated [28].…”

Unique solvability and stability of the time domain electromagnetic scattering problem with a locally perturbed perfectly conducting plate

“…In the time harmonic case, using tools such as Fourier transformation and polarization, analyses of the wave equation and Maxwell's equations are simplified as analyses of the Helmholtz equation [2,3] or the time harmonic Maxwell systems [4,5], which are independent of the time variable and the corresponding scattering problem is usually referred to as a frequency domain problem. A variety of frequency domain scattering problems with unbounded scatterers, such as locally perturbed half-planes [6][7][8][9] and open cavities [10][11][12], have been intensively explored. Newton type methods and sampling methods are considered in [6] and [7], respectively, to solve time harmonic electromagnetic scattering problems in locally perturbed half-planes.…”

“…Stability of time harmonic electromagnetic scattering from two-dimensional large open cavities is investigated in [11]. Integral formulation for electromagnetic scattering from three-dimensional large cavities is provided in [12].…”

Electromagnetic scattering from a cavity embedded in an impedance ground plane

“…() Numerical methods for solving these cavity problems have also been studied extensively; eg, see other works. () Some stability estimates on these cavity problems are given in Li et al, Bao et al, and Kui et al…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] Numerical methods for solving these cavity problems have also been studied extensively; eg, see other works. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] Some stability estimates on these cavity problems are given in Li et al, 28 Bao et al, 31 and Kui et al 32 When cavities are embedded in an imperfect conductor, it can be shown that the electric and magnetic fields at the surface of the conductor satisfy impedance boundary conditions, which are more prevalent in real applications, eg, the detection of a target hidden in a hole on the ground plane and the detection of improvised explosive devices. Although there are a wide range of applications, little mathematical analysis exists for the problem with filled cavities embedded in an impedance ground plane.…”