An improved MFIE formulation for TE-wave scattering from lossy, inhomogeneous dielectric cylinders

Peterson, Andrew F.; Klock, P.

doi:10.1109/8.1073

Cited by 27 publications

(12 citation statements)

References 33 publications

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“…Thus, even though the new integral equations (12) % and (14) have half the unknowns, this was not achieved at the expense of increasing the kernel's singularity or the order of the expansion basis required in their implementation. It is remarked that special forms of these integral equations have already been successfully implemented for two dimensional applications [11,12].…”

Section: Volume Representationsmentioning

confidence: 99%

Alternative field representations and integral equations for modeling inhomogeneous dielectrics

Volakis

1992

IEEE Trans. Microwave Theory Techn.

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Section: Volume Representationsmentioning

confidence: 99%

Alternative field representations and integral equations for modeling inhomogeneous dielectrics

Volakis

1992

IEEE Trans. Microwave Theory Techn.

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“…However, it rapidly appeared that this kind of approximation is not efficient and that it leads to the presence of spurious surface charge densities inside the scatterer [8]. To circumvent this problem, numerical techniques have been developed using the so-called rooftop functions on cells of various shapes [11]- [14]. More recently, to still enhance the accuracy of the MoM, the use of isoparametric elements has been proposed [4].…”

Section: Introductionmentioning

confidence: 99%

The use of the transfinite interpolation in the method of moments applied to electromagnetic scattering by dielectric cylinders

Doncker

2000

IEEE Trans. Antennas Propagat.

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The method of moments (MoM) solution of electromagnetic scattering presents two major numerical difficulties: the number of unknowns and the computation time necessary to calculate the matrix elements. To circumvent these problems, a MoM using the transfinite interpolation and a reduced integration scheme is presented here. The so-called and versions of the new method are applied to the scattering of an electromagnetic wave by an infinite dielectric cylinder (TM case) in the Richmond's formulation. The transfinite and classical methods are compared in terms of the convergence rates of the radar cross section and of the total electric field inside the dielectric. The results confirm the superiority of the new schemes as predicted by the theory.

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“…Although the DIE method (both TM and TE versions of it) has been around in engineering community for many years [16,17,18,19,21,22,25,27,28], the full theoretical analysis of the two-dimensional case (in the strongly singular form) is still missing. The reason might be the presence of special functions in the kernel of the integral operator, which makes calculations more tedious than in the threedimensional case [4,23].…”

Section: Introductionmentioning

confidence: 99%

“…If an object is large and homogeneous or has a perfectly conducting boundary then the problem is usually reduced to a boundary integral equation with the fields (currents) at the interfaces being the fundamental unknowns [13]. If an object is continuously inhomogeneous or is a composite consisting of many small different parts, the most appropriate global method is the domain integral equation (DIE), in two dimensions, or the volume integral equation, in three dimensions [16,17,18,19,21,22,25,27,28]. Although the global methods produce dense matrices, they are generally more stable with respect to discretization than the local ones, and the convolution-type integral operators sometimes allow to compute matrix-vector products at the FFT speed.…”

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confidence: 99%

Transverse Electric Scattering on Inhomogeneous Objects: Spectrum of Integral Operator and Preconditioning

Zouros¹,

Budko²

2012

SIAM J. Sci. Comput.

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Abstract. The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods, especially in the transverse electric (TE) case with large or negative permittivity. We identify the nontrivial essential spectrum of the pertaining integral operator as partly responsible for this behavior, and the main reason why a normally efficient deflating preconditioner does not work. We solve this problem by applying an explicit multiplicative regularizing operator, which transforms the system to the form 'identity plus compact', yet allows the resulting matrix-vector products to be carried out at the FFT speed. Such a regularized system is then further preconditioned by deflating an apparently stable set of eigenvalues with largest magnitudes, which results in a robust acceleration of the restarted GMRES under constraint memory conditions. Key words. Domain integral equation, singular integral operators, electromagnetism, TE scattering, spectrum of operators, essential spectrum, regularizer, deflation, preconditioner AMS subject classifications. 78A45, 65F08, 45E10, 47G10, 15A231. Introduction. There is a steady interest in the numerical simulation of the electromagnetic field in inhomogeneous media. The methods can be roughly divided into two categories -local and global -in accordance with the governing equations. The local methods based on the differential Maxwell's equations [9,10,14,15] are generally more popular due to the sparse nature of their matrices and the ease of programming. Alongside the local methods, global methods based on an equivalent integral equation formulation are also often employed, especially in free-space scattering. If an object is large and homogeneous or has a perfectly conducting boundary then the problem is usually reduced to a boundary integral equation with the fields (currents) at the interfaces being the fundamental unknowns [13]. If an object is continuously inhomogeneous or is a composite consisting of many small different parts, the most appropriate global method is the domain integral equation (DIE), in two dimensions, or the volume integral equation, in three dimensions [16,17,18,19,21,22,25,27,28]. Although the global methods produce dense matrices, they are generally more stable with respect to discretization than the local ones, and the convolution-type integral operators sometimes allow to compute matrix-vector products at the FFT speed. These properties make the DIE method a viable alternative to local methods for certain free-space scattering problems.The main difficulties with the DIE method are the non-normality of both the operator and the resulting system matrix, inherent to frequency-domain electromagnetic scattering, and the extremely slow convergence of the few iterative methods that can be applied with such matrices. Numerical experiments consistently show that the GMRES algorithm is the best choice [11],...

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An improved MFIE formulation for TE-wave scattering from lossy, inhomogeneous dielectric cylinders

Cited by 27 publications

References 33 publications

Alternative field representations and integral equations for modeling inhomogeneous dielectrics

Alternative field representations and integral equations for modeling inhomogeneous dielectrics

The use of the transfinite interpolation in the method of moments applied to electromagnetic scattering by dielectric cylinders

Transverse Electric Scattering on Inhomogeneous Objects: Spectrum of Integral Operator and Preconditioning

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