Coupling of finite element and boundary integral methods for electromagnetic scattering in a two-layered medium

Li, Peijun

doi:10.1016/j.jcp.2009.09.040

Cited by 31 publications

(32 citation statements)

References 33 publications

(30 reference statements)

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“…Note that this condition covers interfaces given by step functions and is thus weaker than the assumption used in Section 4.4. For the Helmholtz and Maxwell equations, the well-posedness results have been established for general locally perturbed flat surfaces which are not necessarily the graph of a function (see [31,34,40]). The arguments rely heavily on properties of the DtN maps derived from the corresponding reflection principle.…”

Section: Case (I)mentioning

confidence: 99%

Elastic scattering from rough surfaces in three dimensions

Zhao

2020

Journal of Differential Equations

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Consider the elastic scattering of a plane or point incident wave by an unbounded and rigid rough surface. The angular spectrum representation (ASR) for the time-harmonic Navier equation is derived in three dimensions. The ASR is utilized as a radiation condition to the elastic rough surface scattering problem. The uniqueness is proved through a Rellich-type identity for surfaces given by uniformly Lipschitz functions. In the case of flat surfaces with a local perturbation, we deduce an equivalent variational formulation in a truncated bounded domain and show the existence results for general incoming waves. The main ingredient of the proof is the radiating behavior of the Green tensor to the first boundary value problem of the Navier equation in a half space.2010 Mathematics Subject Classification. 35A15, 35P25, 74J20.

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Section: Case (I)mentioning

confidence: 99%

Elastic scattering from rough surfaces in three dimensions

Zhao

2020

Journal of Differential Equations

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“…The interior and exterior are finally coupled via the field continuity conditions, leading to a complete system for the solution of interior and surface fields. This technique is particularly attractive for open-region problems involving complex structures and inhomogeneous materials, e.g., Brezzi and Johnson [8], Costable and Stephan [11], Gatica and Hsiao [13], Hsiao [17], Johnson and Nédélec [22], Li [24], Meddahi et al [26].…”

Section: Maxwell's Equationsmentioning

confidence: 99%

Analysis of Direct and Inverse Cavity Scattering Problems

Bao¹

2011

NMTMA

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Consider the scattering of a time-harmonic electromagnetic plane wave by an arbitrarily shaped and filled cavity embedded in a perfect electrically conducting infinite ground plane. A method of symmetric coupling of finite element and boundary integral equations is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases. Given the incident field, the direct problem is to determine the field distribution from the known shape of the cavity; while the inverse problem is to determine the shape of the cavity from the measurement of the field on an artificial boundary enclosing the cavity. In this paper, both the direct and inverse scattering problems are discussed based on a symmetric coupling method. Variational formulations for the direct scattering problem are presented, existence and uniqueness of weak solutions are studied, and the domain derivatives of the field with respect to the cavity shape are derived. Uniqueness and local stability results are established in terms of the inverse problem.

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“…During the last decades many numerical methods for solving Maxwell equations have been developed. Several of them are widely used: the finite-element method (FEM), 1-3 the finite-difference time-domain method (FDTD) 4-6 and the integral equation methods (IEM), which include the boundary element method (BEM) 7,8 and the volume integral method (VIM). [9][10][11][12][13] The enumerated methods are derived from general-purpose numerical discretization schemes.…”

Section: Introductionmentioning

confidence: 99%

Alternative discretization in the aperiodic Fourier modal method leading to reduction in computational costs

Pisarenco

Setija

2013

SPIE Proceedings

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The Fourier modal method (FMM), also referred to as Rigorous Coupled-Wave Analysis (RCWA), is based on Fourier-mode expansions and is inherently built for periodic structures such as diffraction gratings. When the infinite periodicity assumption is not realistic, the finiteness of the structure has to be incorporated into the model. In this paper we discuss the recent extensions of the FMM for finite structures. First, we explain how an efficient FMM-based method for finite structures is obtained by a reformulation of the governing equations and incorporation of perfectly matched layers (PMLs). Then we show that the computational cost of the method can be further reduced by employing an alternative discretization instead of the classical one. Numerical results demonstrate the characteristics of the discussed FMM-based methods and include a discussion of computational complexities.

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Coupling of finite element and boundary integral methods for electromagnetic scattering in a two-layered medium

Cited by 31 publications

References 33 publications

Elastic scattering from rough surfaces in three dimensions

Elastic scattering from rough surfaces in three dimensions

Analysis of Direct and Inverse Cavity Scattering Problems

Alternative discretization in the aperiodic Fourier modal method leading to reduction in computational costs

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