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Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters

Dries Bosman (UGent) , Martijn Huynen (UGent) , Daniël De Zutter (UGent) and Dries Vande Ginste (UGent)
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Abstract
This article presents a novel method to accurately simulate electromagnetic scattering at homogeneous polygonal cylinders with arbitrary material properties. A single source equivalence approach is invoked, allowing to substitute the background medium for the inner material of the scatterer, provided an equivalent surface current density is introduced. We construct the pertinent differential surface admittance operator by means of the Fokas method, establishing a map between the known Dirichlet boundary values and their unknown Neumann counterparts. However, to allow for lossy materials, we extend the Fokas method to complex wavenumbers. The novel formalism, employing pulse-shaped local basis functions, natively supports combined magnetic and dielectric contrast, accurately captures the skin effect, and is conveniently integrated in traditional boundary integral equation formulations. The correctness and versatility of our technique are verified for various examples by means of analytical validation and through comparison with a Poggio-Miller-Chan-Harrington-Wu-Tsai approach, a volume integral equation method and a commercial solver.
Keywords
Differential surface admittance operator, Magnetic materials, Lossy, materials, Boundary integral equations, Electromagnetic scattering, Fokas method, SERIES IMPEDANCE, SKIN

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MLA
Bosman, Dries, et al. “Construction of the Differential Surface Admittance Operator with an Extended Fokas Method for Electromagnetic Scattering at Polygonal Objects with Arbitrary Material Parameters.” COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol. 128, 2022, pp. 44–54, doi:10.1016/j.camwa.2022.10.011.
APA
Bosman, D., Huynen, M., De Zutter, D., & Vande Ginste, D. (2022). Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 128, 44–54. https://doi.org/10.1016/j.camwa.2022.10.011
Chicago author-date
Bosman, Dries, Martijn Huynen, Daniël De Zutter, and Dries Vande Ginste. 2022. “Construction of the Differential Surface Admittance Operator with an Extended Fokas Method for Electromagnetic Scattering at Polygonal Objects with Arbitrary Material Parameters.” COMPUTERS & MATHEMATICS WITH APPLICATIONS 128: 44–54. https://doi.org/10.1016/j.camwa.2022.10.011.
Chicago author-date (all authors)
Bosman, Dries, Martijn Huynen, Daniël De Zutter, and Dries Vande Ginste. 2022. “Construction of the Differential Surface Admittance Operator with an Extended Fokas Method for Electromagnetic Scattering at Polygonal Objects with Arbitrary Material Parameters.” COMPUTERS & MATHEMATICS WITH APPLICATIONS 128: 44–54. doi:10.1016/j.camwa.2022.10.011.
Vancouver
1.
Bosman D, Huynen M, De Zutter D, Vande Ginste D. Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 2022;128:44–54.
IEEE
[1]
D. Bosman, M. Huynen, D. De Zutter, and D. Vande Ginste, “Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol. 128, pp. 44–54, 2022.
@article{01GJQ68AQEP9V8ZRWQJZQ0BN37,
  abstract     = {{This article presents a novel method to accurately simulate electromagnetic scattering at homogeneous polygonal cylinders with arbitrary material properties. A single source equivalence approach is invoked, allowing to substitute the background medium for the inner material of the scatterer, provided an equivalent surface current density is introduced. We construct the pertinent differential surface admittance operator by means of the Fokas method, establishing a map between the known Dirichlet boundary values and their unknown Neumann counterparts. However, to allow for lossy materials, we extend the Fokas method to complex wavenumbers. The novel formalism, employing pulse-shaped local basis functions, natively supports combined magnetic and dielectric contrast, accurately captures the skin effect, and is conveniently integrated in traditional boundary integral equation formulations. The correctness and versatility of our technique are verified for various examples by means of analytical validation and through comparison with a Poggio-Miller-Chan-Harrington-Wu-Tsai approach, a volume integral equation method and a commercial solver.}},
  author       = {{Bosman, Dries and Huynen, Martijn and De Zutter, Daniël and Vande Ginste, Dries}},
  issn         = {{0898-1221}},
  journal      = {{COMPUTERS & MATHEMATICS WITH APPLICATIONS}},
  keywords     = {{Differential surface admittance operator,Magnetic materials,Lossy,materials,Boundary integral equations,Electromagnetic scattering,Fokas method,SERIES IMPEDANCE,SKIN}},
  language     = {{eng}},
  pages        = {{44--54}},
  title        = {{Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters}},
  url          = {{http://doi.org/10.1016/j.camwa.2022.10.011}},
  volume       = {{128}},
  year         = {{2022}},
}

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