Stabilization of Integral-Equation Formulations for the Accurate Solution of Scattering Problems Involving Low-Contrast Dielectric Objects

Ergül, Özgür; Gürel, L.

doi:10.1109/tap.2008.916971

Cited by 14 publications

(14 citation statements)

References 17 publications

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“…We observe that in the form (6) this additional constraint is similar to that used in direct problems to remove spurious resonances [41,42], and essentially as in [35]; in its form (7) it is similar to the approach to re-condition the equation for scattering by dielectric bodies [15,43].…”

Section: Integral Equation Setup and Uniquenessmentioning

confidence: 94%

Field and Source Equivalence in Source Reconstruction on 3d Surfaces

Quijano¹,

Vecchi²

2010

PIER

149

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Abstract-This paper describes in detail different formulations of the inverse-source problem, whereby equivalent sources and/or fields are to be computed on an arbitrary 3-D closed surface from the knowledge of complex vector electric field data at a specified (exterior) surface. The starting point is the analysis of the formulation in terms of the Equivalence Principle, of the possible choices for the internal fields, and of their practical impact. Love's (zero interior field) equivalence is the only equivalence form that yields currents directly related to the fields on the reconstruction surface; its enforcement results in a pair of coupled integral equations. Formulations resulting in a single integral equation are also analyzed. The first is the single-equation, two-current formulation which is most common in current literature, in which no interior field condition is enforced. The single-current (electric or magnetic) formulation deriving from continuity enforcement of one field is also introduced and analyzed. Single-equation formulations result in a simpler implementation and a lower computational load than the dual-equation formulation, but numerical tests with synthetic data support the benefits of the latter. The spectrum of the involved (discretized) operators clearly shows a relation with the theoretical Degrees of Freedom (DoF) of the measured field for the dual-equation formulation that guarantees extraction of these DoF; this is absent in the single-equation formulation. Examples confirm that singleequation formulations do not yield Love's currents, as observed both with comparison with reference data and via energetic considerations. The presentation is concluded with a test on measured data which shows the stability and usefulness of the dual-equation formulation in a situation of practical relevance.

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Section: Integral Equation Setup and Uniquenessmentioning

confidence: 94%

Field and Source Equivalence in Source Reconstruction on 3d Surfaces

Quijano¹,

Vecchi²

2010

PIER

149

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“…These formulations are known as Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) [16][17][18][19], combined tangential formulation (CTF) [14,19], combined normal formulation (CNF) [14,19], modified normal Müller formulation (MNMF) [20], and electric and magnetic current combined-field integral equation (JMCFIE) [9,[21][22][23][24]. Further formulation collections which incorporate other stable formulations can be consulted in [15,19,25,26].…”

Section: A1 Surface Integral Equations For Isolated Bodiesmentioning

confidence: 99%

A computational method for modeling arbitrary junctions employing different surface integral equation formulations for three-dimensional scattering and radiation problems

Gómez‐Sousa

Rubiños-López

Martínez-Lorenzo

et al. 2016

Journal of Electromagnetic Waves and Applications

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This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same simulation, that are in contact with other metallic or dielectric structures. The proposed method for solving the MoM junction problem consists of two separate algorithms, one of which comprises a generalization for bodies in contact of the surface integral equation (SIE) formulations. Unlike some other published SIE generalizations in the field of computational electromagnetics, this generalization does not require duplicating unknowns on the dielectric separation surfaces. Additionally, this generalization is applicable to any ordinary single-scatterer SIE formulations employed as baseline. The other algorithm deals with enforcing boundary conditions and Kirchhoff's Law, relating the surface current flow across a junction edge. Two important features inherent to this latter algorithm consist of a mathematically compact description in matrix form, and, importantly from a software engineering point of view, an easy implementation in existing MoM codes which makes the debugging process more comprehensible. A practical example involving a real grounded monopole antenna for airplane-satellite communication is analyzed for validation purposes by comparing with precise measurements covering different electrical sizes.

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“…In addition, the incident fields due to the external sources satisfy the set of identities [18] tÁ nÂ ( )…”

Section: Low-contrast Breakdown Of Conventional Formulationsmentioning

confidence: 99%

“…Although this is not critical for S-CNF, which already involves identity operators on the LHS, the accuracy of S-CTF can be affected significantly. Therefore, to further improve the accuracy of the T formulation, we can obtain the coefficients x i and y i by solving the discrete form of (13) [18]. This formulation, which is called the double-stabilized CTF (DS-CTF), is completely free of the identity operators at the cost of increased processing time due to the extra solution of the dense equation in (13).…”

Section: ðRþ: ð18þmentioning

confidence: 99%

“…By extracting the nonradiating parts of the currents and solving the modified equations only for the radiating currents (similar to the volume formulations), scattered fields from low-contrast objects can be calculated accurately. Recently, we have applied this procedure to various integral-equation formulations for the solution of three-dimensional problems with arbitrary geometries [16][17][18]. For both the tangential (T) and normal (N) formulations, our stabilization technique involves the expansion of the incident fields in a series of basis functions and the rearrangement of the right-hand sides (RHSs) of the equations.…”

Section: Introductionmentioning

confidence: 99%

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Novel electromagnetic surface integral equations for highly accurate computations of dielectric bodies with arbitrarily low contrasts

Ergül

Gürel

2008

Journal of Computational Physics

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a b s t r a c tWe present a novel stabilization procedure for accurate surface formulations of electromagnetic scattering problems involving three-dimensional dielectric objects with arbitrarily low contrasts. Conventional surface integral equations provide inaccurate results for the scattered fields when the contrast of the object is low, i.e., when the electromagnetic material parameters of the scatterer and the host medium are close to each other. We propose a stabilization procedure involving the extraction of nonradiating currents and rearrangement of the right-hand side of the equations using fictitious incident fields. Then, only the radiating currents are solved to calculate the scattered fields accurately. This technique can easily be applied to the existing implementations of conventional formulations, it requires negligible extra computational cost, and it is also appropriate for the solution of large problems with the multilevel fast multipole algorithm. We show that the stabilization leads to robust formulations that are valid even for the solutions of extremely low-contrast objects.

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Stabilization of Integral-Equation Formulations for the Accurate Solution of Scattering Problems Involving Low-Contrast Dielectric Objects

Cited by 14 publications

References 17 publications

Field and Source Equivalence in Source Reconstruction on 3d Surfaces

Field and Source Equivalence in Source Reconstruction on 3d Surfaces

A computational method for modeling arbitrary junctions employing different surface integral equation formulations for three-dimensional scattering and radiation problems

Novel electromagnetic surface integral equations for highly accurate computations of dielectric bodies with arbitrarily low contrasts

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