Finite Element Methods for Maxwell's Equations

Monk, Peter; Zhang, Yangwen

doi:10.1093/acprof:oso/9780198508885.001.0001

Cited by 1,768 publications

(1,983 citation statements)

References 41 publications

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“…The trace spaces Y (Γ ±h ) are Banach spaces with this norm, see [26]. In the latter reference one also shows that the operation u → ((0, 0,…”

Section: Factorization Of the Near Field Operatormentioning

confidence: 91%

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Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Lechleiter¹,

Nguyen²

2013

SIAM J. Imaging Sci.

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This paper is concerned with the inverse scattering problem of electromagnetic waves from penetrable biperiodic structures in three dimensions. We study the Factorization method as a tool for reconstructing the periodic media from measured data consisting of scattered electromagnetic waves for incident plane electromagnetic waves. We propose a rigorous analysis for the method. A simple criterion is provided to reconstruct the biperiodic structures. We also provide three-dimensional numerical experiments to indicate the performance of the method.

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“…The trace spaces Y (Γ ±h ) are Banach spaces with this norm, see [26]. In the latter reference one also shows that the operation u → ((0, 0,…”

Section: Factorization Of the Near Field Operatormentioning

confidence: 91%

“…Therefore, due to Theorem 3.38 in [26], there exists ψ j ∈ H 1 (Ω h ) 3 such that 3 and we have, in the weak sense,…”

mentioning

confidence: 87%

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Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Lechleiter¹,

Nguyen²

2013

SIAM J. Imaging Sci.

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“…Here h 1 n (r) are spherical Bessel functions of the third kind (Hankel functions), Y m n are spherical harmonics (see, e.g., [12] for details) and a n,m are vector-valued constants. The solution of the acoustic scattering problem satisfies (2.3) as well with E replaced by u and the vector coefficients {a n,m } replaced by scalar coefficients {a n,m }.…”

Section: The Bérenger Layermentioning

confidence: 99%

“…There, they also showed the existence and uniqueness of solutions of the truncated acoustic PML except for a countable number of wave numbers. The formulation of PML equations for (2.1) in spherical coordinates can be found in [12]. Lassas and Somersalo [10] proved the existence and uniqueness of the PML acoustic approximation on a truncated domain where the outer boundary was circular.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems

Bramble

Pasciak

2006

Math. Comp.

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Abstract. We consider the approximation of the frequency domain threedimensional Maxwell scattering problem using a truncated domain perfectly matched layer (PML). We also treat the time-harmonic PML approximation to the acoustic scattering problem. Following work of Lassas and Somersalo in 1998, a transitional layer based on spherical geometry is defined, which results in a constant coefficient problem outside the transition. A truncated (computational) domain is then defined, which covers the transition region. The truncated domain need only have a minimally smooth outer boundary (e.g., Lipschitz continuous). We consider the truncated PML problem which results when a perfectly conducting boundary condition is imposed on the outer boundary of the truncated domain. The existence and uniqueness of solutions to the truncated PML problem will be shown provided that the truncated domain is sufficiently large, e.g., contains a sphere of radius R t . We also show exponential (in the parameter R t ) convergence of the truncated PML solution to the solution of the original scattering problem inside the transition layer.Our results are important in that they are the first to show that the truncated PML problem can be posed on a domain with nonsmooth outer boundary. This allows the use of approximation based on polygonal meshes. In addition, even though the transition coefficients depend on spherical geometry, they can be made arbitrarily smooth and hence the resulting problems are amenable to numerical quadrature. Approximation schemes based on our analysis are the focus of future research.

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Finite Element Methods for M axwell Equations

Demkowicz

2004

Encyclopedia of Computational Mechanics

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The article reviews fundamentals of Finite Element discretizations of time‐harmonic Maxwell equations. The paper includes a short introduction to Maxwell equations, derivation of the standard and regularized variational formulations, discussion of three fundamental Nedelec's elements in context of exact sequences, projection‐based interpolation, and the commuting diagram property. The presentation is biased towards hp ‐discretizations and hp ‐adaptivity.

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Finite Element Methods for Maxwell's Equations

Cited by 1,768 publications

References 41 publications

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems

Finite Element Methods for M axwell Equations

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