Inverse Acoustic and Electromagnetic Scattering Theory

Colton, David; Kreß, Rainer

doi:10.1007/978-1-4614-4942-3

Cited by 1,930 publications

(1,460 citation statements)

References 15 publications

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“…This proves uniqueness (see [10,11]). Note that the operators D k and S k defined on C.@D/ are compact (see [10]).…”

Section: Appendix B Proofs Of Existence and Stability Theoremsmentioning

confidence: 55%

“…/ D r s . n S k .n // D n r S k .n /; see [11]) . Yet the rest of the operators are compact and we can write the operator 1 2 C x x L in (3.51) in the form (B.7) 1 2 …”

Section: Appendix a Flux Conditionmentioning

confidence: 96%

“…It is also well-known that the exterior problem for E scat has a unique solution for ! > 0 when boundary conditions are prescribed on its tangential components (see, for example, [11,25]): (1.9) n E scat .x/ D f.x/ˇ@ D for an arbitrary tangential vector field f. On a perfect conductor, f.x/ D n E inc .x/ to enforce (1.5).…”

Section: The Decoupled Potential Integral Equation For Time-harmonic mentioning

confidence: 99%

“…There are several approaches to overcoming this difficulty. Convergence theorems for Lebesgue integration could be used, as in lemma 3.10 of [11]. Here, we simply use the fact that the function scat j @D is constant on each connected component @D j of @D. Thus, scat j @D 2 C 1;˛.…”

Section: Proof Consider a Solution Of The Homogeneous Problemmentioning

confidence: 99%

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The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Vico

Ferrando

Greengard

et al. 2015

Comm Pure Appl Math

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We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A; in the Lorenz gauge, we establish boundary conditions on the potentials themselves rather than on the field quantities. This permits the development of a wellconditioned second-kind Fredholm integral equation that has no spurious resonances, avoids low-frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, scat , is determined entirely by the incident scalar potential inc . Likewise, the unknown vector potential defining the scattered field, A scat , is determined entirely by the incident vector potential A inc . This decoupled formulation is valid not only in the static limit but for arbitrary ! 0.

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“…This proves uniqueness (see [10,11]). Note that the operators D k and S k defined on C.@D/ are compact (see [10]).…”

Section: Appendix B Proofs Of Existence and Stability Theoremsmentioning

confidence: 55%

“…/ D r s . n S k .n // D n r S k .n /; see [11]) . Yet the rest of the operators are compact and we can write the operator 1 2 C x x L in (3.51) in the form (B.7) 1 2 …”

Section: Appendix a Flux Conditionmentioning

confidence: 96%

Section: The Decoupled Potential Integral Equation For Time-harmonic mentioning

confidence: 99%

Section: Proof Consider a Solution Of The Homogeneous Problemmentioning

confidence: 99%

See 2 more Smart Citations

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

Vico

Ferrando

Greengard

et al. 2015

Comm Pure Appl Math

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“…Following the description of section 3.5 in [7], we recommend the NM based on product quadrature over an equidistant mesh and on trigonometric interpolation. Suppose that the smooth boundary curve Γ D possesses a regular analytic and 2π-periodic parametric representation taking the form…”

Section: Nmmentioning

confidence: 99%

A BIE-Based DtN-FEM for Fluid-Solid Interaction Problems

Yin¹,

Rathsfeld²,

Xu³

2018

JCM

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In this paper, we are concerned with the coupling of finite element methods and boundary integral equation methods solving the classical fluid-solid interaction problem in two dimensions. The original transmission problem is reduced to an equivalent nonlocal boundary value problem via introducing a Dirichlet-to-Neumann mapping by the direct boundary integral equation method. We show the existence and uniqueness of the solution for the corresponding variational equation. Numerical results based on the finite element method coupled with the standard Galerkin boundary element method, the fast multipole method and the Nyström method for approximating the DtN mapping are provided to illustrate the efficiency and accuracy of the numerical schemes.Mathematics subject classification: 65N38, 65N06, 74J05, 76B20.

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Measuring the effect of rounding the corners of scattering structures

Markowskei

Smith

2017

Radio Sci.

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In studying acoustic or electromagnetic wave diffraction, the choice of an appropriate canonical structure to model the dominant features of a scattering scenario can be very illuminating. A common approach used when dealing with domains with corners is to round the corners, producing a smooth surface, eliminating the singularities introduced by the corners. In order to quantify the effect of corner rounding, this paper examines the diffraction from cylindrical scatterers which possess corners, that is, points at which the normal changes discontinuously. We develop a numerical method for the scattering of a plane wave normally incident on such cylindrical structures with soft, hard, or impedance loaded boundary conditions. We then examine the difference between various test structures with corners and with the corners rounded to assess the impact on near‐ and far‐field scattering, as a function of the radius of curvature in the vicinity of the rounded corner point. We then examine the nature of the differences in the far field between the cornered and rounded scatterers as well as the effect on the differences as the frequency of the plane wave increases and obtain precise quantitative estimates for the rate of convergence of the maximum difference between the far‐field solutions as the radius of curvature of the rounded scatterer approaches zero.

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Inverse Acoustic and Electromagnetic Scattering Theory

Cited by 1,930 publications

References 15 publications

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

A BIE-Based DtN-FEM for Fluid-Solid Interaction Problems

Measuring the effect of rounding the corners of scattering structures

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