Numerical Solution of Electromagnetic Scattering Problems Based on the Dirichlet-to-Neumann Map

Maffucci, Antonio; Perrotta, A.; Ventre, Salvatore; Tamburrino, Antonello

doi:10.1109/rtsi.2018.8548371

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…Conversely, for a fixed accuracy, the DtN approach requires much less elements: For instance, a relative error ε = 0.01 would be obtained with N = 501 for DtN and N = 11,305 for PML, hence with a reduction of the DoFs of about 23×. Similar performances may be observed in the case of a single penetrable cylinder, or for arbitrarily shaped scatterers, as shown in [27].…”

Section: Case Study 2: Scattering From a Cable Bundle In Airmentioning

confidence: 56%

“…This entails better insight and more efficient numerical computations. Here we briefly recall its derivation for a circular boundary (details may be found in [15,26,27]). Introducing a polar coordinate system (r, θ) in the x, y plane, the scalar wave equation can be solved in V ext by separation of variables as:…”

Section: The Dirichlet-to-neumann Operatormentioning

confidence: 99%

“…In this paper, the DtN approach is used to solve the scattering problem of a bundled cable illuminated by an external field. The authors have already presented initial results on single scatterers in the conference papers [26,27]. Here, we present the formulation in details, including the analysis of the structure of the matrices associated with the numerical formulation.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Near-Field Analysis of the Electromagnetic Scattering Based on the Dirichlet-to-Neumann Map

et al. 2019

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This paper proposes an efficient technique to solve the electromagnetic scattering problem, in the near zone of scatterers illuminated by external fields. The technique is based on a differential formulation of the Helmholtz equation discretized in terms of a finite element method (FEM). In order to numerically solve the problem, it is necessary to truncate the unbounded solution domain to obtain a bounded computational domain. This is usually done by defining fictitious boundaries where absorbing conditions are imposed, for example by applying the perfect matching layer (PML) approach. In this paper, these boundary conditions are expressed in an analytical form by using the Dirichlet-to-Neumann (DtN) operator. Compared to classical solutions such as PML, the proposed approach based on the DtN: (i) avoids the errors related to approximated boundary conditions; (ii) allows placing the boundary in close proximity to the scatterers, thus, reducing the solution domain to be meshed and the related computational cost; (iii) allows dealing with objects of arbitrary shapes and materials, since the shape of the boundary independent from those of the scatterers. Case-studies on problems related to the scattering from cable bundles demonstrate the accuracy and the computational advantage of the proposed technique, compared to existing ones.

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Section: Case Study 2: Scattering From a Cable Bundle In Airmentioning

confidence: 56%

Section: The Dirichlet-to-neumann Operatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Near-Field Analysis of the Electromagnetic Scattering Based on the Dirichlet-to-Neumann Map

et al. 2019

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3D modeling of coherence scanning interferometry on 2D surfaces using FEM

Pahl¹,

Hagemeier²,

Künne³

et al. 2020

Opt. Express

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Despite the fact that optical profilers, such as coherence scanning interferometers, are frequently used for fast and contactless topography measurements in various fields of application, measured profiles still suffer from the wave characteristics of light, which leads to systematic deviations that are still not sufficiently investigated. In order to analyze these systematic deviations and their physical relations, we apply a rigorous simulation model considering both the transfer characteristics of the measurement instrument as well as the geometry and material of different measurement objects. Simulation results are compared to measurement results for different polarizations, wavelengths and interferometer types, considering surface structures including edges, slopes and different materials as the main reasons for those deviations. Compared to former publications, a full three-dimensional (3D) modeling of the image formation with regard to two-dimensional (2D) surface structures is provided. The advantages of 3D modeling in contrast to a time efficient 2D approach are discussed. Further, an extract of an atomic force microscope (AFM) measurement result is used as the basis for the FEM simulation in one example in order to achieve most realistic simulation results.

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Numerical Solution of Electromagnetic Scattering Problems Based on the Dirichlet-to-Neumann Map

Cited by 2 publications

References 13 publications

Efficient Near-Field Analysis of the Electromagnetic Scattering Based on the Dirichlet-to-Neumann Map

Efficient Near-Field Analysis of the Electromagnetic Scattering Based on the Dirichlet-to-Neumann Map

3D modeling of coherence scanning interferometry on 2D surfaces using FEM

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