Generalized Volume-Surface Integral Equation for Modeling Inhomogeneities Within High Contrast Composite Structures

Usner, B.C.; Sertel, Kubilay; Carr, Michael; Volakis, John L.

doi:10.1109/tap.2005.861579

Cited by 35 publications

(14 citation statements)

References 33 publications

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“…The accuracy has been greatly improved after multiplying c (c = 174547)), and the memory requirements and time are further reduced to 200 and 1039 s, respectively. The result calculated by the EDM-ACA method after preconditioning is in excellent agreement with those of the Mie solution and [6]. So, all the results of the next example are calculated by EDM-ACA after preconditioning.…”

Section: Numerical Resultssupporting

confidence: 73%

“…Figure 2 gives the bistatic RCS for θθ polarization calculated by the Mie, EDM, EDM-ACA and EDM-ACA with a preconditioner (multiplying c (c = 174547)). The results have been compared with that from [6]. The memory needs 263 MB when only EDM is used, and the convergence number is 580, then it cost 2570 s. After employing ACA algorithm, the convergence number is unchanged, but the memory requirements are reduced to 209 MB, then 1295 s are needed.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The memory needs 263 MB when only EDM is used, and the convergence number is 580, then it cost 2570 s. After employing ACA algorithm, the convergence number is unchanged, but the memory requirements are reduced to 209 MB, then 1295 s are needed. However, the results of EDM and EDM-ACA methods have some errors when compared with those of the Mie solution and [6] because of the ill-conditioned impedance matrix. The accuracy has been greatly improved after multiplying c (c = 174547)), and the memory requirements and time are further reduced to 200 and 1039 s, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…However, the SIE is still applicable to piecewise homogeneous media. Therefore, a generalized volume-surface integral equations (GVSIE) [6] method is applied to more effectively analyze the electromagnetic (EM) scattering of high contrast inhomogeneous medium in the paper. The method involves a novel factorization of material parameters that alleviates the computational burden associated with typical VIE implementations.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Fast Volume-Surface Integral Equation Solver for Scattering From High-Contrast Materials

Deng¹,

Gu²,

Xu³

et al. 2012

PIER M

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Abstract-This paper presents a generalized volume-surface integral equation (GVSIE) to solve electromagnetic (EM) scattering of high contrast inhomogeneous materials. Then the method of moments (MoM) is employed to solve the GVSIE. The GVSIE technique where the domain is represented by a corresponding uniform background medium coupled with a variation, together representing the overall inhomogeneity, is solve by the method of moments (MoM) using Schaubert-Wilton-Glisson (SWG) and Rao-Wilton-Glisson (RWG) basis functions. The adaptive cross approximation (ACA) algorithm combined with the equivalent dipole-moment (EDM) method are extended to reduce memory and CPU time. A highly effective preconditioning strategy is presented to solve the system of equations without any increase in the computational complexity. Experiments on several problems representative of scattering simulations are given to illustrate the potential of the above proposed techniques for solving EM scattering involving high contrast applications.

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Section: Numerical Resultssupporting

confidence: 73%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Fast Volume-Surface Integral Equation Solver for Scattering From High-Contrast Materials

Deng¹,

Gu²,

Xu³

et al. 2012

PIER M

View full text Add to dashboard Cite

show abstract

“…Volume integral equations (VIEs) [1] and volume surface integral equations (VSIEs) [2] are often used to fulfill this need. Unfortunately, VIEs suffer from high-contrast (HC) breakdown: when applied to scatterers with electric permittivities that are vastly different from those of the surrounding medium, their discretization results in ill-conditioned systems of equations [3].…”

Section: Introductionmentioning

confidence: 99%

Low-Frequency Stable Internally Combined Volume-Surface Integral Equation for High-Contrast Scatterers

Gomez

Yücel

Michielssen

2015

Antennas Wirel. Propag. Lett.

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Volume integral equations (VIEs) are commonly used to analyze scattering from inhomogeneous dielectric objects. Unfortunately, when VIEs are applied to high-contrast scatterers, their discretization results in ill-conditioned systems of equations. Oftentimes volume-surface integral equations (VSIEs) are used to eliminate this effect. However, when the scatterer's mesh has elements that are much smaller than the wavelength, VSIEs become ill-conditioned, too. This letter introduces a new set of internally combined VSIEs (ICVSIEs) that exhibit neither of these ill-conditioning phenomena. Just like in previous VSIE methods, surface currents are used to artificially increase the effective permittivity of the background medium in which volume polarization currents radiate. To remove ill-conditioning due to electrical size, coupling between the surface and volume is accounted for by judiciously adding contributions due to "exterior" and "interior" surface currents. Numerical data obtained by analyzing time-harmonic TE scattering from various 2-D layered cylinders suggests that discretization of the new ICVSIE yields matrices that are unaffected by the scatterer's maximum permittivity and electrical size. Index Terms-Preconditioner, regularized volume integral equations (VIE), strongly-inhomogenous scatterers.

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Lagrange‐type modeling of continuous dielectric permittivity variation in double‐higher‐order volume integral equation method

2015

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A novel double-higher-order entire-domain volume integral equation (VIE) technique for efficient analysis of electromagnetic structures with continuously inhomogeneous dielectric materials is presented. The technique takes advantage of large curved hexahedral discretization elements-enabled by double-higher-order modeling (higher-order modeling of both the geometry and the current)-in applications involving highly inhomogeneous dielectric bodies. Lagrange-type modeling of an arbitrary continuous variation of the equivalent complex permittivity of the dielectric throughout each VIE geometrical element is implemented, in place of piecewise homogeneous approximate models of the inhomogeneous structures. The technique combines the features of the previous double-higher-order piecewise homogeneous VIE method and continuously inhomogeneous finite element method (FEM). This appears to be the first implementation and demonstration of a VIE method with double-higher-order discretization elements and conformal modeling of inhomogeneous dielectric materials embedded within elements that are also higher (arbitrary) order (with arbitrary material-representation orders within each curved and large VIE element). The new technique is validated and evaluated by comparisons with a continuously inhomogeneous double-higher-order FEM technique, a piecewise homogeneous version of the double-higher-order VIE technique, and a commercial piecewise homogeneous FEM code. The examples include two real-world applications involving continuously inhomogeneous permittivity profiles: scattering from an egg-shaped melting hailstone and near-field analysis of a Luneburg lens, illuminated by a corrugated horn antenna. The results show that the new technique is more efficient and ensures considerable reductions in the number of unknowns and computational time when compared to the three alternative approaches.

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Generalized Volume-Surface Integral Equation for Modeling Inhomogeneities Within High Contrast Composite Structures

Cited by 35 publications

References 33 publications

A Fast Volume-Surface Integral Equation Solver for Scattering From High-Contrast Materials

A Fast Volume-Surface Integral Equation Solver for Scattering From High-Contrast Materials

Low-Frequency Stable Internally Combined Volume-Surface Integral Equation for High-Contrast Scatterers

Lagrange‐type modeling of continuous dielectric permittivity variation in double‐higher‐order volume integral equation method

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