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The Poincaré-Steklov operator in hybrid finite element-boundary integral equation formulations

Pieterjan Demarcke (UGent) and Hendrik Rogier (UGent)
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Abstract
The Poincare-Steklov operator provides a direct relation between the tangential electric and magnetic field at the boundary of a simply connected domain, and a discrete equivalent of the operator can be constructed from the sparse finite element (FE) matrix of that domain by forming the Schur complement to eliminate the interior unknowns. Identifying the FE system matrix as a discretized version of the Poincare-Steklov operator allows us to describe and analyze FE and hybrid finite element-boundary integral equation (FE-BIE) formulations from an operator point of view. We show how this operator notation provides substantial theoretical insight into the analysis of spurious solutions in hybrid FE-BIE methods, and we apply the theory on a TM scattering example to predict the breakdown frequencies of different hybrid formulations.
Keywords
hybrid methods, Electromagnetic scattering, FORM

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Citation

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

Chicago
Demarcke, Pieterjan, and Hendrik Rogier. 2011. “The Poincaré-Steklov Operator in Hybrid Finite Element-boundary Integral Equation Formulations.” Ieee Antennas and Wireless Propagation Letters 10: 503–506.
APA
Demarcke, P., & Rogier, H. (2011). The Poincaré-Steklov operator in hybrid finite element-boundary integral equation formulations. IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, 10, 503–506.
Vancouver
1.
Demarcke P, Rogier H. The Poincaré-Steklov operator in hybrid finite element-boundary integral equation formulations. IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS. 2011;10:503–6.
MLA
Demarcke, Pieterjan, and Hendrik Rogier. “The Poincaré-Steklov Operator in Hybrid Finite Element-boundary Integral Equation Formulations.” IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 10 (2011): 503–506. Print.
@article{2029314,
  abstract     = {The Poincare-Steklov operator provides a direct relation between the tangential electric and magnetic field at the boundary of a simply connected domain, and a discrete equivalent of the operator can be constructed from the sparse finite element (FE) matrix of that domain by forming the Schur complement to eliminate the interior unknowns. Identifying the FE system matrix as a discretized version of the Poincare-Steklov operator allows us to describe and analyze FE and hybrid finite element-boundary integral equation (FE-BIE) formulations from an operator point of view. We show how this operator notation provides substantial theoretical insight into the analysis of spurious solutions in hybrid FE-BIE methods, and we apply the theory on a TM scattering example to predict the breakdown frequencies of different hybrid formulations.},
  author       = {Demarcke, Pieterjan and Rogier, Hendrik},
  issn         = {1536-1225},
  journal      = {IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS},
  keyword      = {hybrid methods,Electromagnetic scattering,FORM},
  language     = {eng},
  pages        = {503--506},
  title        = {The Poincar{\'e}-Steklov operator in hybrid finite element-boundary integral equation formulations},
  url          = {http://dx.doi.org/10.1109/LAWP.2011.2157072},
  volume       = {10},
  year         = {2011},
}

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