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Rigorous analysis of internal resonances in 3-D hybrid FE-BIE formulations by means of the Poincaré-Steklov operator

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Abstract
3-D hybrid finite-element (FE) boundary integral equation (BIE) formulations are widely used because of their ability to simulate large inhomogeneous structures in both open and bounded simulation domains by applying each method where it is the most efficient. However, some formulations suffer from breakdown frequencies at which the solution is not uniquely defined and errors are introduced due to internal resonances. In this paper, we investigate the occurrence of spurious solutions resulting from these resonances by using the concept of the Poincare-Steklov or Dirichlet-to-Neumann operator, which provides a relation between the tangential electric field and the electric current on the boundary of a domain. By identifying this operator in both the FE and BIE method, several new properties of internal resonances in 3-D hybrid FE-BIE formulations are easily derived. Several conformal and nonconformal formulations are studied and the theory is then applied to a scattering problem.
Keywords
INTERIOR RESONANCES, ELECTROMAGNETIC SCATTERING, FINITE-ELEMENT, BOUNDARY-INTEGRAL METHODS, EQUATION, BODIES, MESHES, EFIE, Dirichlet-to-Neumann (DtN), hybrid finite-element boundary-integral equation (FE-BIE), internal resonances, Poincare-Steklov (PS)

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Citation

Please use this url to cite or link to this publication:

Chicago
Boeykens, Freek, Hendrik Rogier, Jan Van Hese, Jeannick Sercu, and Tim Boonen. 2013. “Rigorous Analysis of Internal Resonances in 3-D Hybrid FE-BIE Formulations by Means of the Poincaré-Steklov Operator.” Ieee Transactions on Microwave Theory and Techniques 61 (10): 3503–3513.
APA
Boeykens, F., Rogier, H., Van Hese, J., Sercu, J., & Boonen, T. (2013). Rigorous analysis of internal resonances in 3-D hybrid FE-BIE formulations by means of the Poincaré-Steklov operator. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 61(10), 3503–3513.
Vancouver
1.
Boeykens F, Rogier H, Van Hese J, Sercu J, Boonen T. Rigorous analysis of internal resonances in 3-D hybrid FE-BIE formulations by means of the Poincaré-Steklov operator. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. 2013;61(10):3503–13.
MLA
Boeykens, Freek, Hendrik Rogier, Jan Van Hese, et al. “Rigorous Analysis of Internal Resonances in 3-D Hybrid FE-BIE Formulations by Means of the Poincaré-Steklov Operator.” IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 61.10 (2013): 3503–3513. Print.
@article{4228182,
  abstract     = {3-D hybrid finite-element (FE) boundary integral equation (BIE) formulations are widely used because of their ability to simulate large inhomogeneous structures in both open and bounded simulation domains by applying each method where it is the most efficient. However, some formulations suffer from breakdown frequencies at which the solution is not uniquely defined and errors are introduced due to internal resonances. In this paper, we investigate the occurrence of spurious solutions resulting from these resonances by using the concept of the Poincare-Steklov or Dirichlet-to-Neumann operator, which provides a relation between the tangential electric field and the electric current on the boundary of a domain. By identifying this operator in both the FE and BIE method, several new properties of internal resonances in 3-D hybrid FE-BIE formulations are easily derived. Several conformal and nonconformal formulations are studied and the theory is then applied to a scattering problem.},
  author       = {Boeykens, Freek and Rogier, Hendrik and Van Hese, Jan and Sercu, Jeannick and Boonen, Tim},
  issn         = {0018-9480},
  journal      = {IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES},
  keyword      = {INTERIOR RESONANCES,ELECTROMAGNETIC SCATTERING,FINITE-ELEMENT,BOUNDARY-INTEGRAL METHODS,EQUATION,BODIES,MESHES,EFIE,Dirichlet-to-Neumann (DtN),hybrid finite-element boundary-integral equation (FE-BIE),internal resonances,Poincare-Steklov (PS)},
  language     = {eng},
  number       = {10},
  pages        = {3503--3513},
  title        = {Rigorous analysis of internal resonances in 3-D hybrid FE-BIE formulations by means of the Poincar{\'e}-Steklov operator},
  url          = {http://dx.doi.org/10.1109/TMTT.2013.2277990},
  volume       = {61},
  year         = {2013},
}

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