Exponentially Converging Nystrom Methods in Scattering From Infinite Curved Smooth Strips— Part 2: TE-Case

Time-harmonic electromagnetic wave diffraction by a perfectly electrically conducting (PEC) finite rotationally symmetric surface located in free space is investigated. The problem is split to independent azimuth orders and reduced to the sets of coupled hypersingular and singular integral equations (IEs) for the surface current components. These IEs are discretized by the Nystrom-type method of discrete singularities using the interpolation type quadrature formulas. From the solutions of corresponding matrix equations the near-and the far-field patterns are obtained. The presented method has guaranteed convergence for arbitrary not axially symmetric primary field.Index Terms-Body of revolution (BOR), focusing, interpolation type quadrature formulas, radar cross-section, scattering, singular and hypersingular integral equations.

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“…We use the following interpolation type quadrature formulas [12]- [14], [31] for discretization of HSIE and SIE (28):…”

Section: Discretization Of Iesmentioning

confidence: 99%

“…The alternative to MAR is the meshless Nystrom-type numerical algorithms having guaranteed convergence and developed recently for 2-D problems [11], [12], [31]. Here, the current density is sought as a product of unknown smooth function and known weight.…”

Section: Introductionmentioning

confidence: 99%

Nystrom-Type Method in Three-Dimensional Electromagnetic Diffraction by a Finite PEC Rotationally Symmetric Surface

Bulygin

Nosich

Gandel³

2012

IEEE Trans. Antennas Propagat.

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“…On solving the matrix equations we obtain approximate solutions to our SIEs in the form of interpolation polynomials for the unknown surface currents. The quadrature formulas ensure rapid convergence of the approximate solutions to the accurate ones (for the proof, see [18]- [23]) if and , respectively.…”

Section: A Discretization Using the Quadraturesmentioning

confidence: 99%

“…The last of the mentioned guarantees convergence of numerical solutions and provides 3-4 digit accuracy with a relatively small number of unknowns. Besides, recently the Nystrom-type numerical techniques using the quadratures and interpolation-based discretization have attracted attention of researchers [18]- [23]. They have been already demonstrated as convergent, economic and simple in implementation for the modeling of the scattering by PEC zero-thickness flat and curved strips [20]- [27].…”

Section: Introductionmentioning

confidence: 99%

Scattering and Absorption of Waves by Flat Material Strips Analyzed Using Generalized Boundary Conditions and Nystrom-Type Algorithm

Shapoval

Sauleau

Nosich

2011

IEEE Trans. Antennas Propagat.

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The scattering of the H-and E-polarized plane waves by a thin flat homogeneous magneto-dielectric strip is considered. Assuming the strip to be thinner than the wavelength, we shrink its cross-section to the median line where the generalized boundary conditions are imposed. The numerical solution is built on two singular integral equations discretized using Nystrom-type numerical algorithm. The obtained results demonstrate fast convergence and good agreement with data known for the limiting values of the strip parameters. This opens a way to the accurate numerical analysis of various striplike configurations simulating natural objects and electromagnetic circuit components, both in traditional microwave applications and nanophotonics.Index Terms-Discrete mathematical model, generalized two-side boundary conditions, scattering cross-sections, singular and hyper-singular integral equations, strip scatterer.

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“…There are many publications that present mathematical models of wave scattering and diffraction that are based on the use of different methods for solving corresponding problems [1][2][3][4][5][6][7][8][9][10]. However, there exist constraints on the application of some of these methods, which are connected with the range of their parameters, and some other methods are insufficiently efficient.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model of Wave Scattering by an Impedance Grating1

Kostenko

2015

Cybern Syst Anal

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This article develops a numerical-analytical method for solving the problem of scattering acoustic and electromagnetic waves by an impedance grating. This problem leads to a third-type boundary problem for the two-dimensional Helmholtz equation with additional conditions. The boundary value problem is reduced to boundary integral equations, and the discrete singularities method is modified to numerically solve them. Dependencies of integral characteristics of solutions to the problem on frequency are obtained.

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Exponentially Converging Nystrom Methods in Scattering From Infinite Curved Smooth Strips— Part 2: TE-Case

Cited by 20 publications

References 7 publications

Nystrom-Type Method in Three-Dimensional Electromagnetic Diffraction by a Finite PEC Rotationally Symmetric Surface

Nystrom-Type Method in Three-Dimensional Electromagnetic Diffraction by a Finite PEC Rotationally Symmetric Surface

Scattering and Absorption of Waves by Flat Material Strips Analyzed Using Generalized Boundary Conditions and Nystrom-Type Algorithm

Mathematical Model of Wave Scattering by an Impedance Grating1

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