Novel Monopolar MFIE MoM-Discretization for the Scattering Analysis of Small Objects

Úbeda, Eduard; Rius, J.M.

doi:10.1109/tap.2005.861529

Cited by 88 publications

(58 citation statements)

References 17 publications

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“…These efforts include increasing the accuracy of the MFIE matrix elements [11], [12], incorporating a solid angle contribution [13] or enriching the finite element space [14], [15]. The aforementioned techniques have been demonstrated to result in a significant accuracy improvement when applied to certain classes of scattering problems.…”

mentioning

confidence: 99%

Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

Bogaert

Cools

Andriulli

et al. 2014

IEEE Trans. Antennas Propagat.

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Abstract-The standard and mixed discretizations for the Magnetic Field Integral Equation (MFIE) and the Müller Integral Equation (MUIE) are investigated in the context of lowfrequency (LF) scattering problems involving simply connected scatterers. It is proved that, at low frequencies, the frequency scaling of the nonsolenoidal part of the solution current can be incorrect for the standard discretization. In addition, it is proved that the frequency scaling obtained with the mixed discretization is correct. The reason for this problem in the standard discretization scheme is the absence of exact solenoidal currents in the rotated RWG finite element space. The adoption of the mixed discretization scheme eliminates this problem and leads to a well-conditioned system of linear equations that remains accurate at low frequencies. Numerical results confirm these theoretical predictions and also show that, when the frequency is lowered, a finer and finer mesh is required to keep the accuracy constant with the standard discretization.

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mentioning

confidence: 99%

Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

Bogaert

Cools

Andriulli

et al. 2014

IEEE Trans. Antennas Propagat.

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“…The b 1,ρ term, in contrast, with non-zero divergence, must provide for the expansion of the nonsolenoidal subspace of current. Furthermore, the monopolar RWG discretization of the MFIE reduces significantly the RCS deviation observed with the RWG discretization for moderately small sharp-edged objects [10]. Since the div-TO basis functions expand the same space as the monopolar RWG set, it is reasonable to expect some improvement in the div-TO discretization of the EMFIE too with respect to the Loop-Star discretization.…”

Section: Taylor-orthogonal Discretization Of the Electric-magnetic Fimentioning

confidence: 98%

“…The properties (10) and (14) show that these basis functions are orthogonal, whereby we name them Taylor-orthogonal basis functions. We define two sets of Taylor-orthogonal basis functions: the divergence-Taylor-orthogonal basis functions (div-TO) and the curl- Taylor The monopolar RWG and nxRWG sets [10,24] stand for facetoriented sets of basis functions too.…”

Section: Taylor-orthogonal Basis Functionsmentioning

confidence: 99%

“…We define two sets of Taylor-orthogonal basis functions: the divergence-Taylor-orthogonal basis functions (div-TO) and the curl- Taylor The monopolar RWG and nxRWG sets [10,24] stand for facetoriented sets of basis functions too. They arise from breaking, respectively, the normal or tangential continuity constraints enforced by the RWG or nxRWG sets across the edges.…”

Section: Taylor-orthogonal Basis Functionsmentioning

confidence: 99%

“…This discrepancy is especially evident in the analysis of electrically moderately small perfectly conducting sharp-edged objects. Over the last years, other sets of basis functions have been proposed for the MoM-discretization of the MFIE in the scattering analysis of PeCobjects that reduce the observed discrepancy [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Taylor-Orthogonal Basis Functions for the Discretization in Method of Moments of Second Kind Integral Equations in the Scattering Analysis of Perfectly Conducting or Dielectric Objects

Farré¹,

Palau²,

Rius³

2011

PIER

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Abstract-We present new implementations in Method of Moments of two types of second kind integral equations: (i) the recently proposed Electric-Magnetic Field Integral Equation (EMFIE), for perfectly conducting objects, and (ii) the Müller formulation, for homogeneous or piecewise homogeneous dielectric objects. We adopt the Taylororthogonal basis functions, a recently presented set of facet-oriented basis functions, which, as we show in this paper, arise from the Taylor's expansion of the current at the centroid of the discretization triangles. We show that the Taylor-orthogonal discretization of the EMFIE mitigates the discrepancy in the computed Radar Cross Section observed in conventional divergence-conforming implementations for moderately small, perfectly conducting, sharp-edged objects. Furthermore, we show that the Taylor-discretization of the Müller-formulation represents a valid option for the analysis of sharpedged homogenous dielectrics, especially with low dielectric contrasts, when compared with other RWG-discretized implementations for dielectrics. Since the divergence-Taylor Orthogonal basis functions are facet-oriented, they appear better suited than other, edge-oriented, discretization schemes for the analysis of piecewise homogenous objects since they simplify notably the discretization at the junctions arising from the intersection of several dielectric regions.

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2014

The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large‐Scale Computational Electromagnetics Problems

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Novel Monopolar MFIE MoM-Discretization for the Scattering Analysis of Small Objects

Cited by 88 publications

References 17 publications

Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

Low-Frequency Scaling of the Standard and Mixed Magnetic Field and Müller Integral Equations

Taylor-Orthogonal Basis Functions for the Discretization in Method of Moments of Second Kind Integral Equations in the Scattering Analysis of Perfectly Conducting or Dielectric Objects

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