Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering

Contopanagos, Harry; Dembart, B.; Epton, Michael A.; Ottusch, John J.; Rokhlin, Vladimir; Visher, J.L.; Wandzura, Stephen M.

doi:10.1109/tap.2002.803956

Cited by 156 publications

(136 citation statements)

References 8 publications

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“…We have explained, in Section 5, how to do this for partial wave expansions, plane waves, and (of course) the potentials induced by known impressed currents and charges. We have also developed integral representations for [15], the Calderon preconditioning combined source integral equation (CP-CSIE) [12], and the regularized combined source integral equation (RCSIE) [7]. the vector and scalar potentials that lead to well-conditioned second kind integral equations (the decoupled potential integral equations or DPIE).…”

Section: Discussionmentioning

confidence: 99%

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Vico

Ferrando

Greengard

et al. 2015

Comm Pure Appl Math

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We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A; in the Lorenz gauge, we establish boundary conditions on the potentials themselves rather than on the field quantities. This permits the development of a wellconditioned second-kind Fredholm integral equation that has no spurious resonances, avoids low-frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, scat , is determined entirely by the incident scalar potential inc . Likewise, the unknown vector potential defining the scattered field, A scat , is determined entirely by the incident vector potential A inc . This decoupled formulation is valid not only in the static limit but for arbitrary ! 0.

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Section: Discussionmentioning

confidence: 99%

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Vico

Ferrando

Greengard

et al. 2015

Comm Pure Appl Math

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“…A way to solve this problem is to precondition the EFIE operator T not with the operator T itself, but with its localized counterpart. This localization can be obtained either by a space windowing the Green's function [4] or by using, in the leftmost operator T , a purely complex wavenumber, as was proposed in [5], obtaining…”

Section: Background and Formula-tionmentioning

confidence: 99%

A well-conditioned combined field integral equation based on quasi-helmholtz projectors

Andriulli

Bogaert²,

Cools

et al. 2013

2013 International Conference on Electromagnetics in Advanced Applications (ICEAA)

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-We introduce a novel combined field integral equation that does not suffer from internal resonances and solves several drawbacks of existing resonance-free formulations. The new equation is obtained by combining a regularized electric type operator with a new magnetic type operator that exhibits uniform frequency scaling when acting on, or being tested within, the harmonic Helmholtz subspace for surface currents. With an appropriate use of quasi-Helmholtz projectors, the equation is stable for arbitrarily low-frequencies. Numerical results confirm the theoretical developments and show the effectiveness of the scheme.

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“…Among others, combined field integral equation (CFIE) formulation, i.e., a judiciously constructed linear combinations of EFIE and MFIE [8,9], is largely preferred [2,[10][11][12][13][14][15][16][17][18]. The desired uniqueness property of such a kind of formulation resides in the orthogonality of the null spaces of EFIE and MFIE formulations.…”

Section: Introductionmentioning

confidence: 99%

“…The problem is even worse for scatterers with edges or corners due to the divergence of the fields on geometrical singularities. As a matter of fact, the second kind MFIE related to the longitudinal current is ill-posed since the functional spaces to which the unknown and the free term belong are different [2,11].…”

Section: Introductionmentioning

confidence: 99%

Fast Converging Cfie-Mom Analysis of Electromagnetic Scattering From Pec Polygonal Cross-Section Closed Cylinders

Lucido¹,

Murro²,

Panariello³

et al. 2017

PIER B

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Abstract-The analysis of the electromagnetic scattering from perfectly electrically conducting (PEC) objects with edges and corners performed by means of surface integral equation formulations has drawbacks due to the interior resonances and divergence of the fields on geometrical singularities. The aim of this paper is to show a fast converging method for the analysis of the scattering from PEC polygonal cross-section closed cylinders immune from the interior resonance problems. The problem, formulated as combined field integral equation (CFIE) in the spectral domain, is discretized by means of Galerkin method with expansion functions reconstructing the behaviour of the fields on the wedges with a closed-form spectral domain counterpart. Hence, the elements of the coefficients' matrix are reduced to single improper integrals of oscillating functions efficiently evaluated by means of an analytical asymptotic acceleration technique.

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Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering

Cited by 156 publications

References 8 publications

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

A well-conditioned combined field integral equation based on quasi-helmholtz projectors

Fast Converging Cfie-Mom Analysis of Electromagnetic Scattering From Pec Polygonal Cross-Section Closed Cylinders

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