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On a well-conditioned electric field integral operator for multiply connected geometries

Francesco P. Andriulli, Kristof Cools, Ignace Bogaert (UGent) and Eric Michielssen
(2013) IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. 61(4). p.2077-2087
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Abstract
All known integral equation techniques for simulating scattering and radiation from arbitrarily shaped, perfect electrically conducting objects suffer from one or more of the following shortcomings: (i) they give rise to ill-conditioned systems when the frequency is low (ii) and/or when the discretization density is high, (iii) their applicability is limited to the quasi-static regime, (iv) they require a search for global topological loops, (v) they suffer from numerical cancellations in the solution when the frequency is very low. This work presents an equation that does not suffer from any of the above drawbacks when applied to smooth and closed objects. The new formulation is obtained starting from a Helmholtz decomposition of two discretizations of the electric field integral operator obtained by using RWGs and dual bases respectively. The new decomposition does not leverage Loop and Star/Tree basis functions, but projectors that derive from them. Following the decomposition, the two discretizations are combined in a Calderon-like fashion resulting in a new overall equation that is shown to exhibit self-regularizing properties without suffering from the limitations of existing formulations. Numerical results show the usefulness of the proposed method both for closed and open structures.
Keywords
DOMAIN CALDERON IDENTITIES, LOOP-STAR DECOMPOSITION, ELECTROMAGNETIC SCATTERING, EQUATION ANALYSIS, LOW-FREQUENCIES, EFIE, PRECONDITIONER, OBJECTS, ALGORITHM, SURFACES, Calderon equations, integral equations, loop-star/tree bases, MFIE

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Citation

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

MLA
Andriulli, Francesco P., et al. “On a Well-Conditioned Electric Field Integral Operator for Multiply Connected Geometries.” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol. 61, no. 4, 2013, pp. 2077–87, doi:10.1109/TAP.2012.2234072.
APA
Andriulli, F. P., Cools, K., Bogaert, I., & Michielssen, E. (2013). On a well-conditioned electric field integral operator for multiply connected geometries. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, 61(4), 2077–2087. https://doi.org/10.1109/TAP.2012.2234072
Chicago author-date
Andriulli, Francesco P., Kristof Cools, Ignace Bogaert, and Eric Michielssen. 2013. “On a Well-Conditioned Electric Field Integral Operator for Multiply Connected Geometries.” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 61 (4): 2077–87. https://doi.org/10.1109/TAP.2012.2234072.
Chicago author-date (all authors)
Andriulli, Francesco P., Kristof Cools, Ignace Bogaert, and Eric Michielssen. 2013. “On a Well-Conditioned Electric Field Integral Operator for Multiply Connected Geometries.” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 61 (4): 2077–2087. doi:10.1109/TAP.2012.2234072.
Vancouver
1.
Andriulli FP, Cools K, Bogaert I, Michielssen E. On a well-conditioned electric field integral operator for multiply connected geometries. IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. 2013;61(4):2077–87.
IEEE
[1]
F. P. Andriulli, K. Cools, I. Bogaert, and E. Michielssen, “On a well-conditioned electric field integral operator for multiply connected geometries,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol. 61, no. 4, pp. 2077–2087, 2013.
@article{4228017,
  abstract     = {{All known integral equation techniques for simulating scattering and radiation from arbitrarily shaped, perfect electrically conducting objects suffer from one or more of the following shortcomings: (i) they give rise to ill-conditioned systems when the frequency is low (ii) and/or when the discretization density is high, (iii) their applicability is limited to the quasi-static regime, (iv) they require a search for global topological loops, (v) they suffer from numerical cancellations in the solution when the frequency is very low. This work presents an equation that does not suffer from any of the above drawbacks when applied to smooth and closed objects. The new formulation is obtained starting from a Helmholtz decomposition of two discretizations of the electric field integral operator obtained by using RWGs and dual bases respectively. The new decomposition does not leverage Loop and Star/Tree basis functions, but projectors that derive from them. Following the decomposition, the two discretizations are combined in a Calderon-like fashion resulting in a new overall equation that is shown to exhibit self-regularizing properties without suffering from the limitations of existing formulations. Numerical results show the usefulness of the proposed method both for closed and open structures.}},
  author       = {{Andriulli, Francesco P. and Cools, Kristof and Bogaert, Ignace and Michielssen, Eric}},
  issn         = {{0018-926X}},
  journal      = {{IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION}},
  keywords     = {{DOMAIN CALDERON IDENTITIES,LOOP-STAR DECOMPOSITION,ELECTROMAGNETIC SCATTERING,EQUATION ANALYSIS,LOW-FREQUENCIES,EFIE,PRECONDITIONER,OBJECTS,ALGORITHM,SURFACES,Calderon equations,integral equations,loop-star/tree bases,MFIE}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{2077--2087}},
  title        = {{On a well-conditioned electric field integral operator for multiply connected geometries}},
  url          = {{http://doi.org/10.1109/TAP.2012.2234072}},
  volume       = {{61}},
  year         = {{2013}},
}
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