The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Vico, Felipe; Ferrando, M.; Greengard, Leslie; Gimbutas, Zydrunas

doi:10.1002/cpa.21585

Cited by 63 publications

(60 citation statements)

References 33 publications

(100 reference statements)

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“…Some of these pros are also pointed in [56] . It is to be noted that for some problems, when ω → 0, the A equation will capture the magnetoquasistatic solutions well.…”

Section: Pec Scatterer Casementioning

confidence: 93%

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Chew¹

2014

PIER

122

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Abstract-The mixed vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The present rapid development in quantum optics applications calls for electromagnetic solutions that straddle both the quantum and classical physics regimes. The vector potential formulation using A and Φ (or A-Φ formulation) is a good candidate to bridge these two regimes. Hence, there is a need to generalize this formulation to inhomogeneous media. A generalized gauge is suggested for solving electromagnetics problems in inhomogenous media that can be extended to the anistropic case. An advantage of the resulting equations is their absence of catastrophic breakdown at low-frequencies. Hence, the usual differential equation solvers can be used to solve them over a wide range of scales and bandwidth. It is shown that the interface boundary conditions from the resulting equations reduce to those of classical Maxwell's equations. Also, the classical Green's theorem can be extended to such a formulation, resulting in an extinction theorem and a surface equivalence principle similar to the classical case. Moreover, surface integral equation formulations can be derived for piecewise homogeneous scatterers. Furthermore, the integral equations neither exhibit the low-frequency catastrophe nor the frequency imbalance observed in the classical formulation using E-H fields. The matrix representation of the integral equation for a PEC (perfect electric conductor) scatterer is given.

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“…Some of these pros are also pointed in [56] . It is to be noted that for some problems, when ω → 0, the A equation will capture the magnetoquasistatic solutions well.…”

Section: Pec Scatterer Casementioning

confidence: 93%

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Chew¹

2014

PIER

122

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“…Finally in Sec. VII we show that our field-only formulation does not suffer from the well-documented numerical instability at the zero frequency or long wavelength limit that is inherent in all current boundary integral formulation of electromagnetic scattering 10,11 , so that our results will reduce uniformly to the correct static limit. Thus our boundary integral formulation provides a theoretically and numerically robust resolution to the so called zero frequency catastrophe.…”

Section: Introductionmentioning

confidence: 69%

“…Thus this formulation is not robust in the multiscale sense if the characteristic length scale of the problem becomes much smaller than the wavelength. This is an unsurprising result because in the long wavelength or electrostatic limit, the electric and magnetic fields decouple and the electric field should be described in terms of the charge density rather than the current density 11 .…”

Section: Stratton-chu Boundary Integral Formulationmentioning

confidence: 99%

Robust multiscale field-only formulation of electromagnetic scattering

2017

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We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and magnetic, H fields and with the scalar functions (r · E) and (r · H), the problem can be cast as having to solve a set of scalar Helmholtz equations for the field components that are coupled by the usual electromagnetic boundary conditions at material boundaries. This facilitates a direct solution for the surface values of E and H rather than having to work with surface currents or surface charge densities as intermediate quantities in existing methods. Consequently, our formulation is free of the well-known numerical instability that occurs in the zero frequency or long wavelength limit in traditional surface integral solutions of Maxwell's equations and our numerical results converge uniformly to the static results in the long wavelength limit. Furthermore, we use a formulation of the scalar Helmholtz equation that is expressed as classically convergent integrals and does not require the evaluation of principal value integrals or any knowledge of the solid angle. Therefore, standard quadrature and higher order surface elements can readily be used to improve numerical precision for the same number of degrees of freedom. In addition, near and far field values can be calculated with equal precision and multiscale problems in which the scatterers possess characteristic length scales that are both large and small relative to the wavelength can be easily accommodated. From this we obtain results for the scattering and transmission of electromagnetic waves at dielectric boundaries that are valid for any ratio of the local surface curvature to the wave number. This is a generalization of the familiar Fresnel formula and Snell's law, valid at planar dielectric boundaries, for the scattering and transmission of electromagnetic waves at surfaces of arbitrary curvature. Implementation details are illustrated with scattering by multiple perfect electric conductors as well as dielectric bodies with complex geometries and composition.

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“…To this end, several new SIE formulations and numerical techniques have been proposed; a partial listing of these includes the current and charge integral equation (CCIE) [9], augmented EFIE (A-EFIE) [13], Calderón preconditioner [14], multi-resolution analysis [15] and introducing loop-tree/star basis functions [7], [8], [16]- [18], and Debye sources [19]- [21]. Recently, a decoupled potential integral equation (DPIE) based on Lorentz gauge has been proposed in [22] that leads to a second-kind and stable formulation over a wide frequency band. DPIE was implemented numerically by using Nyström method in [23].…”

Section: Introductionmentioning

confidence: 99%

Generalized Debye Sources-Based EFIE Solver on Subdivision Surfaces

Jiang

et al. 2017

IEEE Trans. Antennas Propagat.

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Abstract-The electric field integral equation is a well known workhorse for obtaining fields scattered by a perfect electric conducting (PEC) object. As a result, the nuances and challenges of solving this equation have been examined for a while. Two recent papers motivate the effort presented in this paper. Unlike traditional work that uses equivalent currents defined on surfaces, recent research proposes a technique that results in well conditioned systems by employing generalized Debye sources (GDS) as unknowns. In a complementary effort, some of us developed a method that exploits the same representation for both the geometry (subdivision surface representations) and functions defined on the geometry, also known as isogeometric analysis (IGA). The challenge in generalizing GDS method to a discretized geometry is the complexity of the intermediate operators. However, thanks to our earlier work on subdivision surfaces, the additional smoothness of geometric representation permits discretizing these intermediate operations. In this paper, we employ both ideas to present a well conditioned GDS-EFIE. Here, the intermediate surface Laplacian is well discretized by using subdivision basis. Likewise, using subdivision basis to represent the sources, results in an efficient and accurate IGA framework. Numerous results are presented to demonstrate the efficacy of the approach.

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The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Cited by 63 publications

References 33 publications

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Robust multiscale field-only formulation of electromagnetic scattering

Generalized Debye Sources-Based EFIE Solver on Subdivision Surfaces

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