Logarithmic Integral Equations in Electromagnetics

Shestopalov, Yury; Smirnov, Yu. G.; Chernokozhin, E. V.

doi:10.1515/9783110942057

Cited by 32 publications

(32 citation statements)

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“…and u = (u 1 , u 2 ) denotes the vector of displacements. Introduce the trace operators L (1) and L (2) specifying the boundary conditions on ω, ω * and Γ :…”

Section: Approximate Decompositionmentioning

confidence: 99%

“…The operator Lu = L (1) u + L (2) u specifies the boundary conditions of problem A in the form Lu = f , with f = (0, f 2 (x)) and…”

Section: Approximate Decompositionmentioning

confidence: 99%

“…The processes which take place in layered structures may be described in terms of boundary value problems (BVPs) for elliptic systems [1,2], among them are the Laplace, Helmholtz, and Lamè equations, equipped with appropriate boundary conditions of mixed type, including boundary-value contact problems (BVCPs) formulated and investigated in [3].…”

Section: Introductionmentioning

confidence: 99%

“…The simplest examples of BVPs with boundary conditions of mixed type in electromagnetics and acoustics [1,2] arise when the Dirichlet (or Neumann) conditions are stated on one part of the boundary and the Neumann (Dirichlet) condition on its complement. Such problem are formulated, e. g., in mathematical models of the wave propagation in transmission lines [1]. A decomposition for the solution to the BVPs for the equation systems can be applied when the differential operator can be separated while the boundary value (trace) operators are mixed componentwise on the boundary.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Decomposition for the Solution of Boundary Value Problems for Elliptic Systems Arising in Mathematical Models of Layered Structures

Shestopalov¹,

Kotik²

2006

PIERS Online

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We present an alternative approach to the solution of boundary value problems (BVPs) for elliptic systems arising in mathematical models of layered structures. The main idea of the method is to consider auxiliary problems for differential operators separated componentwise and to reduce them to a sequence of iterative problems such that each can be solved (explicitly) by the Fourier method. The solution sequence is then constructed with the help of a contracting transfer operator evaluated explicitly. This method facilitates both analytic and numerical solutions and can be generalized to more complicated mixed BVPs for semilinear partial differential operators.

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“…and u = (u 1 , u 2 ) denotes the vector of displacements. Introduce the trace operators L (1) and L (2) specifying the boundary conditions on ω, ω * and Γ :…”

Section: Approximate Decompositionmentioning

confidence: 99%

“…The operator Lu = L (1) u + L (2) u specifies the boundary conditions of problem A in the form Lu = f , with f = (0, f 2 (x)) and…”

Section: Approximate Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximate Decomposition for the Solution of Boundary Value Problems for Elliptic Systems Arising in Mathematical Models of Layered Structures

Shestopalov¹,

Kotik²

2006

PIERS Online

View full text Add to dashboard Cite

show abstract

“…The second technique is an exponentially converging Galerkin method (GM) detailed in [6] and [7]: the underlying principle is the use of Chebyshev polynomials for the regularization of singular integral operators, an idea that has been elaborated in several works, initially in mechanics and subsequently in electromagnetics, see [8] and [9] and references therein.…”

Section: Introductionmentioning

confidence: 99%

TM and TE Diffraction by a Perfectly Conducting Half-Plane in Presence of a Perfectly Conducting Strip: Solution by Exponentially Converging Nystrom and Galerkin Methods

Tsalamengas

2008

IEEE Trans. Antennas Propagat.

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We study TM and TE diffraction by a perfectly conducting half-plane in presence of a perfectly conducting flat strip of finite width and infinite length; the edges of the strip are parallel to the edge of the half-plane. The relevant integral equations with unknowns the induced current densities on the strip are solved by a Nyström and a Galerkin method that fully account for the singular nature of the kernels and the singularities of the solution at the edges. The proposed algorithms are highly accurate, and appear to converge exponentially as shown by detailed numerical examples and case studies. The Nyström method is the most efficient of the two methods because of its simple formulation, fast computer implementation, and much less effort in computing the matrix elements. When the strip is coplanar to the half-plane, an additional formulation method in terms of equivalent surface magnetic currents is possible in the framework of the field equivalence principles. This alternative method is applied in order to validate the algorithms and test their accuracy.

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Boundary Hybrid Galerkin Method for Elliptic and Wave Propagation Problems in ℝ3 over Planar Structures

Jerez-Hanckes

Nédélec

2009

Integral Methods in Science and Engineering, Volume 2

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Logarithmic Integral Equations in Electromagnetics

Cited by 32 publications

References 0 publications

Approximate Decomposition for the Solution of Boundary Value Problems for Elliptic Systems Arising in Mathematical Models of Layered Structures

Approximate Decomposition for the Solution of Boundary Value Problems for Elliptic Systems Arising in Mathematical Models of Layered Structures

TM and TE Diffraction by a Perfectly Conducting Half-Plane in Presence of a Perfectly Conducting Strip: Solution by Exponentially Converging Nystrom and Galerkin Methods

Boundary Hybrid Galerkin Method for Elliptic and Wave Propagation Problems in ℝ3 over Planar Structures

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