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## The determination of the surface conductivity of a partially coated dielectric

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Venue: | SIAM J. Appl. Math |

Citations: | 19 - 9 self |

### Citations

1051 | Inverse acoustic and electromagnetic scattering theory,”
- Colton
- 2003
(Show Context)
Citation Context ... the scatterer has the same magnetic permeability µ0 as the exterior medium but the electric permittivity ɛ and the conductivity σ are real 3 × 3 matrix valued functions. After an appropriate scaling =-=[12]-=-, the total electric and magnetic fields E,H satisfy the time-harmonic homogeneous Maxwell equations in the exterior of the scatterer, (2.1) { ∇×E − ikH =0, ∇×H + ikE =0, and the interior electric and... |

1033 |
A Perfectly Matched Layer for the Absorptions of Electromagnetic Waves,”
- Berenger
- 1994
(Show Context)
Citation Context ... then employing a near to far field transformation [18]. The finite element computational domain is terminated by a rectilinear perfectly matched layer using a linear absorption function in the layer =-=[2, 10]-=-. Having computed approximate values of the far field pattern at N uniformly spaced points on the unit circle for N incoming waves we have an N × N matrix A of approximate far field data Am,n = uh,∞(d... |

492 | Strongly elliptic systems and boundary integral equations.
- McLean
- 2000
(Show Context)
Citation Context ...(Γ2) := {u ∈ H 1 2 (Γ2) : supp u ⊆ Γ2}, 1 − and denote by H 2 (Γ2) and ˜ � � ′ � 1 1 − H 2 (Γ2) the dual spaces ˜H 2 (Γ2) and H 1 � ′ 2 (Γ2) , respectively, with L 2 as a pivot space (for details see =-=[16]-=-). We recall that a function in ˜ H 1 2 (Γ2) and ˜ 1 − H 2 (Γ2) can be extended by zero to a function in H 1 2 (Γ) and H 1 2 (Γ), respectively. For later use we also define the Hilbert space H 1 (D, Γ... |

363 | Finite Element Methods for Maxwell’s Equations - Monk - 2003 |

85 | The perfectly matched layer in curvilinear coordinates
- Collino, Monk
- 1998
(Show Context)
Citation Context ... then employing a near to far field transformation [18]. The finite element computational domain is terminated by a rectilinear perfectly matched layer using a linear absorption function in the layer =-=[2, 10]-=-. Having computed approximate values of the far field pattern at N uniformly spaced points on the unit circle for N incoming waves we have an N × N matrix A of approximate far field data Am,n = uh,∞(d... |

52 |
A simple method using Morozov's discrepancy principle for solving inverse scattering problems. Inverse Problems
- Colton, Piana, et al.
- 1477
(Show Context)
Citation Context ...re bm = Nγ exp(−ik(z · dm))/(2π), 1 ≤ m ≤ N. This ill conditioned problem is solved approximately using the Tikhonov regularization and the Morozov discrepancy principle as described, for example, in =-=[14]-=-. 6.1. Exact knowledge of the boundary. We start as in [5] assuming an exact knowledge of the boundary in order to assess the accuracy of (4.17) without the added error of computing an approximation t... |

43 |
The linear sampling method in inverse electromagnetic scattering theory. Inverse problems
- Colton, Haddar, et al.
- 2003
(Show Context)
Citation Context ...reduce the radar cross section of the scattered wave. In [5] it was shown that the solution of the far field equation that determines the shape of the scatterer by means of the linear sampling method =-=[11]-=- can also be used in conjunction with a variational method to determine the essential supremum of the surface impedance of the coated portion of the boundary and numerical examples were given showing ... |

34 | The direct and inverse scattering problems for partially coated obstacles
- Cakoni, Colton, et al.
- 2001
(Show Context)
Citation Context ...n of the first kind of order zero. A reconstruction of D can be obtained by using the linear sampling method which characterizes the support D from a solution of the far field equation (4.5) (see e.g =-=[3]-=-, [7]). Assuming that D is known our goal is to provide a formula for computing the L∞ norm of η in terms of the solution of the far field equation (4.5). To this end, assuming that k is not an transm... |

31 |
On the uniqueness of the shape of a penetrable, anisotropic obstacle
- Hähner
- 2000
(Show Context)
Citation Context ...) → H 2 (SR) which maps h ∈ H 1 2 (SR) to ∂ũ ∂ν where ũ solves the exterior Dirichlet problem for the Helmholtz equation in R2 \ BR with Dirichlet boundary data h. The following result is known [12], =-=[15]-=-. Lemma 3.2. There exist an operator Λ0 : H 1 1 2 − (SR) → H 2 (SR) such that � ϕ Λ0ϕ ds ≤ 0 (3.1) SR and Λ − Λ0 is a compact operator from H 1 1 2 − (SR) to H 2 (SR). Integrating by parts the equatio... |

30 | The linear sampling method for anisotropic media, J.Comput
- Cakoni, Colton, et al.
(Show Context)
Citation Context ...+ f|Γ2 + r on Γ2 (v) ∂v − ∂νA ∂w = h ∂ν on Γ In the sequel we will refer to (3.5) as (IMTP). The well posedness of the interior transmission problem in the case when η ≡ 0 and r = 0 is established in =-=[7]-=-. We will adapt here the variational approach used in [7] to our mixed transmission case. In order to avoid repetition we will only sketch the proof, emphasizing the changes due to the boundary terms ... |

26 | The Adaptive Computation of Far-Field Patterns by A Posteriori Error Estimation of Linear Functionals,
- Monk, Suli
- 1998
(Show Context)
Citation Context ...the Helmholtz equation. For a given scatterer, the far field data is computed by using a cubic finite element code to approximate the near field, and then employing a near to far field transformation =-=[18]-=-. The finite element computational domain is terminated by a rectilinear perfectly matched layer using a linear absorption function in the layer [2, 10]. Having computed approximate values of the far ... |

23 | The determination of the surface impedance of a partially coated obstacle from far field data
- Cakoni, Colton
(Show Context)
Citation Context ...ing problem, interior transmission problem, electromagnetic waves, mixed boundary value problems. AMS subject classifications. 35P25, 35R30, 78A45 1. Introduction. In a previous paper in this journal =-=[5]-=-, we considered the problem of determining the surface impedance of a perfect conductor that is partially coated by a dielectric from a knowledge of the far field pattern of the scattered electromagne... |

17 | Combined far field operators in electromagnetic inverse scattering theory - Cakoni, Colton |

17 | A uniqueness theorem for an inverse electromagnetic scattering problem in inhomogeneous anisotropic media.
- Cakoni, Colton
- 2003
(Show Context)
Citation Context ...) ) ɛ(x)+i ω . Let the real valued function η>0 defined on the coated portion of the boundary of the scatterer describe the physical properties of the highly conductive coating (see [1]). As shown in =-=[8]-=-, the tangential component of the electric field is continuous across the boundary (2.3) ν × E − ν × E0 =0, while the tangential component of the magnetic field is continuous only on the uncoated part... |

12 |
The conductive boundary condition for Maxwell’s equations
- Angell, Kirsch
- 1992
(Show Context)
Citation Context ...= 1 ɛ0 � ɛ(x) + i σ(x) ω (2.2) Let the real valued function η > 0 defined on the coated portion of the boundary of the scatterer describe the physical properties of the highly conductive coating (see =-=[1]-=-). As shown in [8] the tangential component of the electric field is continuous across the boundary ν × E − ν × E0 = 0 (2.3) while the tangential component of magnetic field is continuous only on the ... |

11 |
2003 A uniqueness theorem for an inverse electomagnetic scattering problem in inhomogeneous anisotropic media Proc
- Cakoni, Colton
(Show Context)
Citation Context ...σ(x) ω (2.2) Let the real valued function η > 0 defined on the coated portion of the boundary of the scatterer describe the physical properties of the highly conductive coating (see [1]). As shown in =-=[8]-=- the tangential component of the electric field is continuous across the boundary ν × E − ν × E0 = 0 (2.3) while the tangential component of magnetic field is continuous only on the uncoated part of t... |

11 |
Eigenvalues of the far field operator and inverse scattering theory
- Colton, Kress
- 1995
(Show Context)
Citation Context ...2) ∂Φ(·, z1) Φ(·, z1) − Φ(·, z2) ds ∂ν ∂ν Γ � � ds + � Φ(·, z1) ∂wz2 � ∂Φ(·, z1) − wz2 ds. ∂ν ∂ν Green’s theorem applied to the radiating solution Φ(·, z) of the Helmholtz equation in De implies that =-=[13]-=- � � � � ∂Φ(·, z2) ∂Φ(·, z1) Φ(·, z1) − Φ(·, z2) ds = −2ik Φ∞(·, z1)Φ∞(·, z2)ds ∂ν ∂ν Ω Γ � = −2ik |γ| 2 e −ikˆx·z1 e ikˆx·z2 ds = −4ikπ|γ| 2 J0(k|z1 − z2|) D Ω and from the representation formula for... |

6 | Combined far field operatots in electromagnetic inverse scattering theory - Cakoni, Colton |

1 | A target signature for distinguishing perfect conductors from anisotropic media of finite conductivity
- Cakoni, Colton
(Show Context)
Citation Context ...sider the problem complementary to the one described above; i.e., we now wish to detect a benign object that has been partially coated by a thin conducting material in order to make it appear hostile =-=[6]-=-. An example of this is a wooden decoy in the shape of a tank that is partially coated by metallic paint. The problem is again to determine a coefficient (the surface conductivity) in the boundary con... |