Improving the accuracy of the surface integral equations for low-contrast dielectric scatterers

We consider the solution of electromagnetic scattering problems involving relatively large dielectric objects with moderate and low contrasts. Three-dimensional objects are discretized with Rao-Wilton-Glisson functions and the scattering problems are formulated with surface integral equations. The resulting dense matrix equations are solved iteratively by employing the multilevel fast multipole algorithm. We compare the accuracy and efficiency of the results obtained by employing various integral equations for the formulation of the problem. If the problem size is large, we show that a combined formulation, namely, electric-magnetic current combined-field integral equation, provides faster iterative convergence compared to other formulations, when it is accelerated with an efficient block preconditioner. For low-contrast problems, we introduce various stabilization procedures in order to avoid the numerical breakdown encountered in the conventional surface formulations. © 2007 IEEE

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“…Extracting the nonradiating currents and rearranging the equation, we obtain the stable CTF (S-CTF) as [16] t ·…”

Section: Low-contrast Breakdown and Stabilization Of Surface Formumentioning

confidence: 99%

Fast and accurate solutions of scattering problems involving dielectric objects with moderate and low contrasts

Ergül

Gürel

2007

2007 Computational Electromagnetics Workshop

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“…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%

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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“…Considering in (5), applying a stabilization procedure, and using the identity (20) we obtain a stable CTF (S-CTF) as…”

Section: Stabilization Of Surface Formulationsmentioning

confidence: 99%

“…Although this is not critical for S-CNF, which already contains identity operators, the accuracy of S-CTF can be significantly affected. Therefore, to obtain more accurate results, we propose a double-stabilized CTF (DS-CTF) based on calculating the coefficients related to the incident fields by solving the discretized form of (20), i.e., (41) where (42) (43) We note that the improved accuracy of DS-CTF comes at the cost of reduced efficiency since it is necessary to solve an additional dense matrix equation rather than the extremely sparse equation in (40).…”

Section: Imentioning

confidence: 99%

“…As a consequence, scattered fields cannot be calculated accurately using the traditional forms of the surface integral equations. For accurate solutions, surface formulations should be modified by extracting the known nonradiating currents from the total currents and considering only the radiating currents as the unknowns of the problem [11], [20].…”

Section: Surface Formulations Of Dielectric Problemsmentioning

confidence: 99%

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

Ergül

Gürel

2008

IEEE Trans. Antennas Propagat.

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Abstract-The solution of scattering problems involving low-contrast dielectric objects with three-dimensional arbitrary shapes is considered. Using the traditional forms of the surface integral equations, scattered fields cannot be calculated accurately if the contrast of the object is low. Therefore, we consider the stabilization of the formulations by extracting the nonradiating parts of the equivalent currents. We also investigate various types of stable formulations and show that accuracy can be improved systematically by eliminating the identity terms from the integral-equation kernels. Traditional and stable formulations are compared, not only for small scatterers but also for relatively large problems solved by employing the multilevel fast multipole algorithm. Stable and accurate solutions of dielectric contrasts as low as 10 4 are demonstrated on problems involving more than 250000 unknowns.Index Terms-Dielectrics, electromagnetic scattering, multilevel fast multipole algorithm (MLFMA), surface integral equations.

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Improving the accuracy of the surface integral equations for low-contrast dielectric scatterers

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Cited by 4 publications

References 7 publications

Fast and accurate solutions of scattering problems involving dielectric objects with moderate and low contrasts

Fast and accurate solutions of scattering problems involving dielectric objects with moderate and low contrasts

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

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

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