### Citations

457 |
Integral Equation Methods in Scattering Theory. Pure and Applied Mathematics
- Colton, Kress
- 1983
(Show Context)
Citation Context ...that (I − Mκ − CκΛ) is a Fredholm operator of index zero. Kress first proposed a compact regularization Λj = n × S 2 0j where S0 is the single layer boundary integral operator of the Laplace equation =-=[3]-=-, thus (I + Mκ + CκΛ) is a Fredhom operator of the second kind. One can also use the elliptic and invertible operator Λj = C0j which is a variant of the operator Cκ [5, 22] defined on H C0j = n × S0j ... |

40 | Constructive Approximation on the Sphere - Freeden, Gervens, et al. - 1998 |

37 | Logarithmic convergence rates of the iteratively regularized Gauß—Newton method for an inverse potential and an inverse scattering problem. Inverse Problems - Hohage - 1997 |

27 |
I.G.: A high-order algorithm for obstacle scattering in three dimensions
- Ganesh, Graham
- 2004
(Show Context)
Citation Context ...ithm The parametrized boundary integral equations (3.6) and (3.7) are now propicious to obtain spectrally accurate approximations of the solution by combining the spectral method of Ganesh and Graham =-=[7]-=- and the hybrid spectral method of Ganesh and Hawkins [10, 11]. The numerical scheme is based on the numerical integration formula over the unit sphere for a continuous function ∫ 2n+1 ∑ n+1 ∑ u(x)ds... |

16 | Acoustic and Electromagnetic Equations, Vol 144 - Nédélec - 2001 |

13 |
Electromagnetic waves scattering : Scattering by obstacles, Scattering
- Kress
- 2001
(Show Context)
Citation Context ...y the obvious formulas F ′[q]ξ = (F ′ 1[q]ξ, . . . , F ′ m[q]ξ) T and F ′[q]* h = ∑m k=1 F ′ k [q]* h. The following theorem is a rewriting, for the electric field only, of the theorem established in =-=[16]-=- by Kress. Theorem 5.1 (characterization of F ′ [q]). The mapping F : Q → L 2 t (S 2 ) with s > 2 is Fréchet differentiable at all q ∈ Q for which Γq is of class C 2 , and the first derivative at q in... |

7 | Fast Methods for Three-Dimensional Inverse Obstacle Scattering. Preprint 35/2005, Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen - Harbrecht, Hohage - 2005 |

6 | On the Kleinman-Martin integral equation method for the electromagnetic scattering problem by a dielectric
- Costabel, Louër
- 2009
(Show Context)
Citation Context ...perator of the Laplace equation [3], thus (I + Mκ + CκΛ) is a Fredhom operator of the second kind. One can also use the elliptic and invertible operator Λj = C0j which is a variant of the operator Cκ =-=[5, 22]-=- defined on H C0j = n × S0j + curlΓ S0 divΓ j. Γ 1 − 2 div (Γ) by The far-field pattern can be computed via the integral representation formula E ∞ = F∞j where − 1 2 the far-field operator F∞ : Hdiv (... |

6 |
fields on spheres
- Vector
- 1962
(Show Context)
Citation Context ...2013 for j = −l, . . . , l and l = 0, 1, 2, . . . form a complete orthonormal system in L 2 (S 2 ). The formula (4.1) is exact for the spherical polynomials of order less than or equal to 2n + 1 (see =-=[20]-=-). This induces the discrete inner product (·, ·)n (ϕ1, ϕ2)n = 2n+1 ∑ n+1 ∑ µρντ ϕ1(xρτ )ϕ2(xρτ ), ρ=0 τ=1 on the space Pn of all scalar spherical polynomials of degree less than or equal to n. We h... |

5 |
Domain derivatives in electromagnetic scattering
- Potthast
- 1996
(Show Context)
Citation Context ...ncorporated in the IRGNM to compute the far-field pattern of the solution and its derivative at each iteration steps. In electromagnetism, Fréchet differentiability was first investigated by Potthast =-=[21]-=- for the perfect conductor problem, using the boundary integral equation approach. The characterization of the first derivative was then improved by Kress [16]. In section 5, we formulate the IRGNM fo... |

5 |
Modified combined field integral equations for electromagnetic scattering
- Steinbach, Windisch
(Show Context)
Citation Context ...perator of the Laplace equation [3], thus (I + Mκ + CκΛ) is a Fredhom operator of the second kind. One can also use the elliptic and invertible operator Λj = C0j which is a variant of the operator Cκ =-=[5, 22]-=- defined on H C0j = n × S0j + curlΓ S0 divΓ j. Γ 1 − 2 div (Γ) by The far-field pattern can be computed via the integral representation formula E ∞ = F∞j where − 1 2 the far-field operator F∞ : Hdiv (... |

4 | On a convergence problem of the iterative-regularized Gauss-Newton method, Zh Vychisl Mat i Mat Fiz 32 (9 - Bakushinskiı̆ - 1992 |

3 |
A spectrally accurate algorithm for electromagnetic scattering in three dimensions
- Ganesh, Hawkins
(Show Context)
Citation Context ...e approximation of the solution to the forward problem. Among all the existing numerical methods to solve integral equations, we focus here on spectral methods. Ganesh and Hawkins already proposed in =-=[8, 9, 10, 11]-=- several spectrally accurate methods to implement the electric field integral equation (EFIE). One of them [11] consists in transporting the EFIE on the unit sphere via a normal transformation acting ... |

3 |
Simple equations giving shapes of various convex polyhedra: the regular polyhedra and polyhedra composed of crystallographically low-index planes
- Onaka
- 2006
(Show Context)
Citation Context ...y an off center point source located inside the perfect conductor : E inc (x) = grad Φ(κ, |x − s|) × p, s ∈ Ω and p ∈ S 2 . 11Table 1: Parametric representation of the perfectly conducting obstacles =-=[1, 18]-=- surface parametric representation sphere q ◦ ψ(θ, φ) = Rψ(θ, φ), R ∈ R ∗ + ; great stellated dodecahedron q ◦ ψ(θ, φ) = 0.33 r(θ, φ)ψ(θ, φ), where r(θ, φ) > 0 solves p−|r(θ,φ)f(δ,ξ,0)|p + p−|r(θ,φ)f(... |

1 | version 1 - hal-00780379 - 2013 |

1 |
compounds, periodicity and the exponential scale
- Andersson, Stellations
- 2004
(Show Context)
Citation Context ...y an off center point source located inside the perfect conductor : E inc (x) = grad Φ(κ, |x − s|) × p, s ∈ Ω and p ∈ S 2 . 11Table 1: Parametric representation of the perfectly conducting obstacles =-=[1, 18]-=- surface parametric representation sphere q ◦ ψ(θ, φ) = Rψ(θ, φ), R ∈ R ∗ + ; great stellated dodecahedron q ◦ ψ(θ, φ) = 0.33 r(θ, φ)ψ(θ, φ), where r(θ, φ) > 0 solves p−|r(θ,φ)f(δ,ξ,0)|p + p−|r(θ,φ)f(... |

1 |
Louër, A spectrally accurate method for the dielectric obstacle scattering problem and applications to the inverse problem, in preparation
- Hohage, Le
- 2012
(Show Context)
Citation Context ... splitting of the various singularities. The fully discrete high order spectral algorithm and numerical examples are presented in section 4. The Piola transform is already used by Hohage and Le Louër =-=[15]-=- to implement systems of second-kind boundary integral equations in an inverse dielectric obstacle scattering algorithm. Therefore, section 3 and 4 use notations and contain various results from [15] ... |

1 | Spektralrandintegralmethoden zur Maxwell-Gleichung - Pieper - 2007 |