MFIE MoM-formulation with curl-conforming basis functions and accurate kernel integration in the analysis of perfectly conducting sharp-edged objects

Úbeda, Eduard; Rius, J.M.

doi:10.1002/mop.20633

Cited by 68 publications

(49 citation statements)

References 9 publications

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“…contains more information, than the one with p ′ . Therefore, statements like (6) in this paper will be intended to give the strongest scaling that can be proved for a general geometry, complex permittivity, etcetera.…”

Section: Lf Behavior Of Integral Operatorsmentioning

confidence: 99%

“…plates) and, when using the standard discretization strategy, they offer inferior accuracy when compared to equations of the first kind [6]. Nevertheless, second kind integral equations are of great practical importance because of their role in the Combined Field Integral Equation (CFIE) and because they yield wellconditioned systems of linear equations without special preconditioning strategies (e.g.…”

mentioning

confidence: 99%

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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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Section: Lf Behavior Of Integral Operatorsmentioning

confidence: 99%

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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“…Interestingly, the imposition of the tangential continuity of the current across edges appears better-suited than the imposition of the normal continuity for the MoM-discretization of the MFIE for sharp-edged objects [6]. The normal-continuity constraint in RWG is applied in the discretizations of the EFIE but it is not clear, in our opinion, that it must be imposed for second kind Integral Equations like the MFIE or the EMFIE.…”

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%

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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“…Recently, the main focus of the studies on the accuracy of the magnetic-field integral equation (MFIE) for low-order discretizations of perfect conductors has shifted to a proper choice of the testing functions [1], instead of a complete change of the basis and testing functions [2][3][4][5][6]. For example, it is shown that using the rotated Buffa-Christiansen (nBC) functions [7] instead of the conventional Rao-WiltonGlisson (RWG) functions [8] can significantly improve the accuracy of MFIE to the levels of the electricfield integral equation (EFIE).…”

Section: Introductionmentioning

confidence: 99%

Numerical Constructions of Testing Functions for Improving the Accuracy of Mfie and Cfie in Multi-Frequency Applications

Karaosmanoğlu¹,

Altinoklu²,

Ergul³

2016

PIER M

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Abstract-We present a new approach based on numerical constructions of testing functions for improving the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) with low-order discretizations. Considering numerical solutions, testing functions are designed by enforcing the compatibility of the MFIE systems with the accurate coefficients obtained by solving the electric-field integral equation (EFIE). We demonstrate the accuracy improvements on scattering problems, where the testing functions are designed at a single frequency and used in frequency ranges to benefit from the design procedure. The proposed approach is easy to implement by using existing codes, while it improves the accuracy of MFIE and CFIE without deteriorating the efficiency of iterative solutions.

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MFIE MoM-formulation with curl-conforming basis functions and accurate kernel integration in the analysis of perfectly conducting sharp-edged objects

Cited by 68 publications

References 9 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

Numerical Constructions of Testing Functions for Improving the Accuracy of Mfie and Cfie in Multi-Frequency Applications

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