New numerical-analytical methods in diffraction theory

Poyedinchuk, A. Ye.; Tuchkin, Yury A.; Shestopalov, V. P.

doi:10.1016/s0895-7177(00)00188-6

Cited by 49 publications

(42 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A brief explanation of the principal ideas of ARM can be found in [15], and their detailed description is the subject of a book [18]. The freshest explanation of the ARM methodology by Yu.…”

Section: Appendix Amentioning

confidence: 99%

“…These faults are more pronounced in the resonant domain, which is of great interest to technical applications. The idea of Analytical Regularization Method (ARM) can be utilized for mathematically equivalent transformation of a first-kind operator equation to a second-kind Fredholm equation, which allows efficient numerical solution with preassigned accuracy [3,[15][16][17]. The brief explanation of the principal ideas of ARM is presented in Appendix.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Diffraction From a Grating on a Chiral Medium: Application of Analytical Regularization Method

Panin¹,

Turetken²,

Poyedinchuk³

et al. 2014

PIER B

View full text Add to dashboard Cite

Abstract-Theoretical results on the electromagnetic wave diffraction from a periodic strip grating placed on a chiral medium are obtained. Analytical Regularization Method based on the solution to the vector Riemann-Hilbert boundary value problem was used to get robust numerical results in the resonant domain, where direct solution methods typically fail. It was shown that in the case of normal incidence of linearly polarized wave the cross-polarized field appears in the reflected field. For elliptically polarized incident wave the diffraction character essentially depends on the polarization direction of the incident wave. These diffraction peculiarities are more pronounced in the resonant domain. Influence of the dichroism caused by chiral medium losses is thoroughly studied. The combination of a chiral medium and a grating can be effectively used for a frequency and polarization selection and for a mode conversion.

show abstract

Section: Appendix Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Diffraction From a Grating on a Chiral Medium: Application of Analytical Regularization Method

Panin¹,

Turetken²,

Poyedinchuk³

et al. 2014

PIER B

View full text Add to dashboard Cite

show abstract

“…In particular, K(ξ,ζ) is continuous with its first derivatives and all its mixed derivatives of the second order are squareintegrable. L(ξ,ζ) is the logarithmic function which is the most singular part in (1). Interval [-d,d] is for the variable of contour parameterization that is either [-π,π) for closed contour or [-1,1] for unclosed contour reason of which will follows.…”

Section: B Canonical Integral Equation With Logarithmic Singularity mentioning

confidence: 99%

“…We use below the following Kronecker's delta δ sn definitions given by means of exponent function for closed contour or orthonormal Chebyshev's polynomials of the first kind for unclosed contour: (2) Following expansions for L(ξ,ζ) can be found in [1] for closed contours (cc) and in [3] for unclosed contours (uc): …”

Section: B Canonical Integral Equation With Logarithmic Singularity mentioning

confidence: 99%

“…Analytical regularization method (ARM) is a mathematically rigorous methodology to solve wave diffraction problems concerning rather wide class of canonical surfaces [1]. When Fredholm integral equations of the first kind are considered, discretizing them lead to algebraic system of the first kind and their solutions require additional attention for their validation [2].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rigorous solution by analytical regularization method to the problem of 2D E-Polarized wave diffraction by a set of PEC surfaces

Yigit

Dikmen

Suvorova

et al. 2009

2009 Computational Electromagnetics International Workshop

View full text Add to dashboard Cite

The analytical regularization method is applied to the problem of 2D E-Polarized wave diffraction by perfectly conductive surfaces consisting of a set of closed and unclosed surfaces. The electromagnetic boundary value problem is reduced to the infinite algebraic system of the second kind which in principal can be solved with any predetermined accuracy by means of truncation procedure. Numerical results, including condition number behavior, current density, and field's space distribution for obstacles are presented.

show abstract

Well-conditioned algorithm for scattering by a few eccentrically multilayered dielectric circular cylinders

et al. 2015

View full text Add to dashboard Cite

The new regularization of the well-known analytical formulation of the monochromatic electromagnetic wave scattering by a few eccentrically multilayered homogenous circular cylinders is presented. It is found out that a regularization of this formulation is absolutely necessary. The two-sided regularization that we made is based on the integral formulation of the mentioned problem. The polarization of the fields are parallel to the longitudinal axes of the cylinders; thus, a two dimensional problem for each both polarizations are under consideration. The condition number of the resulting algebraic system is uniformly bounded while its truncation number increases. The numerical results are validated by existing results such as near and far fields obtained under various geometrical and electrical parameters of the scattering problem. Numerical results including the condition numbers of the regularized and nonregularized systems show that only regularized system gives numerically stable results with any desired accuracy in a wide range of frequencies from quasistatic to rather high-frequency range, limited only by the capabilities of the computer with the guarantee of the physical reliability of the solution.

show abstract

New numerical-analytical methods in diffraction theory

Cited by 49 publications

References 2 publications

Diffraction From a Grating on a Chiral Medium: Application of Analytical Regularization Method

Diffraction From a Grating on a Chiral Medium: Application of Analytical Regularization Method

Rigorous solution by analytical regularization method to the problem of 2D E-Polarized wave diffraction by a set of PEC surfaces

Well-conditioned algorithm for scattering by a few eccentrically multilayered dielectric circular cylinders

Contact Info

Product

Resources

About