Novel Buffa-Christiansen Functions for Improving CFIE With Impedance Boundary Condition

Li, Weidong; Wang, Hong; Zhou, Haibo; Song, Zhe

doi:10.1109/tap.2012.2201121

Cited by 12 publications

(9 citation statements)

References 21 publications

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“…The IBC3 involves the discretization of the surface divergence of n× RWG functions. This problem has been circumvented in [16] for the IBC0 and in [12] for the IBC3 by using Buffa-Christianssen functions that, however, increase the computational cost. Instead, the computationally very cheap div2curl and curl2div transformations [10,11,17] are employed here, and the costly inversion of a full impedance matrix involved in the formulation proposed in [11] is suppressed.…”

Section: Introductionmentioning

confidence: 99%

A Well-Posed and Effective High-Order Impedance Boundary Condition for the Time-Harmonic Scattering Problem From a Multilayer Coated 3-D Object

Stupfel¹,

Payen²,

Lafitte³

2021

PIER B

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The time-harmonic scattering problem from an isotropic multilayer coated 3-D object is considered. The coating is modeled by an impedance boundary condition (IBC) prescribed on the outer surface of the coating. The standard Leontovich IBC is local and constitutes a poor approximation for low index materials. A possible remedy is to employ high order IBCs (HOIBCs) involving tangential differential operators multiplied by coefficients. A generic HOIBC formulation (termed here IBC3) with five coefficients is considered here. Sufficient uniqueness conditions (SUCs) are derived for the corresponding Maxwell's problem (i.e., Maxwell's equations in free-space, radiation condition at infinity and IBC3 on the surface). The IBC3 coefficients are obtained by minimizing, with the SUCs as constraints, the error between either the exact and IBC3 impedances (local planar approximation) or the exact and IBC3 Mie series coefficients (local spherical approximation). Finally, the IBC3 is numerically implemented in a well-posed EFIE+MFIE formulation. Numerical results obtained on 3D objects demonstrate the high accuracy achieved with the constrained IBC3.

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Section: Introductionmentioning

confidence: 99%

A Well-Posed and Effective High-Order Impedance Boundary Condition for the Time-Harmonic Scattering Problem From a Multilayer Coated 3-D Object

Stupfel¹,

Payen²,

Lafitte³

2021

PIER B

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“…There are two unknowns on each RWG element [10] corresponding to J and M. As a result, the MoM matrix equations of the discretized SIEs are memory-consuming and the iteration solutions are time-consuming, which would be the bottleneck for large-scale EM problems. Various fast methods such as the fast Fourier transform (FFT) [11], the adaptive integral method (AIM) [12] and the multilevel fast multipole algorithm (MLFMA) [6], [8], [13]- [17], [22]- [29] have been developed. The MLFMA is one of the great breakthroughs of computational electromagnetics (CEM), and it reduces the computation time and memory requirement to O(NlogN ) for a matrix-vector multiplication (MVM) [13], where N is the number of degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

A Concise and Efficient MLFMA Scheme for Electromagnetic Surface Integral Equations From Dielectric Objects

Miao

Wang

2020

IEEE Access

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In the surface field integral equations (SIEs) from three-dimensional homogeneous dielectric objects, the equivalence electric and magnetic currents on the discontinuous interfaces between different homogeneous media are two independent sources. When the SIEs are iteratively solved, as indicated by the published literatures, the multilevel fast multipole algorithm (MLFMA) needs to be implemented respectively for the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) with these two currents, and hence a few MLFMA implementations are necessary for each homogeneous medium. In this paper, a concise and efficient scheme is proposed for reducing the implementations of the SIEs-MLFMA. First, the summation of the EFIE and MFIE-MLFMA implementations with the two currents can be simplified into one EFIE or MFIE-MLFMA implementation with integrating electric and magnetic currents at the lowest-level aggregation stage. Secondly, the common matrix frameworks consisting of the EFIE and MFIE-MLFMA implementations used in the SIEs can be simplified into one MLFMA implementation with two lowest-level diaggregations. The enhanced MLFMA scheme has excellent applicability to eight kinds of SIEs in wide use. In this way, the resulted SIE-MLFMA scheme performs only once for each homogeneous medium when transforming outgoing wave expansions of the two currents into incoming wave expansions for bottom cubes. Compared with the widely-used implementation approach of the MLFMA one by one for the two currents, it reduces the computation complexity by one half without sacrificing accuracy and adding a little memory requirement. Some examples are presented to validate the enhanced MLFMA scheme.

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“…This technique is widespread and is known to provide accurate models of scattering in a wide variety of scenarios. This notwithstanding several recent contributions have sensibly advanced the original integral equation approach by proposing combined field formulations [4], discretizations based on dual elements [5], self-dual schemes [6], and generalized impedance boundary conditions [7], [8].…”

Section: Introductionmentioning

confidence: 99%

“…Equation (5) is classically known as impedance boundary condition. Using (5) in the first equation of (1) results in the Impedance Boundary Condition EFIE (IBC-EFIE)…”

Section: Introductionmentioning

confidence: 99%

An Impedance Boundary Condition EFIE That Is Low-Frequency and Refinement Stable

Dély

Andriulli

Cools

2017

IEEE Trans. Antennas Propagat.

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Dely, Alexandre and Andriulli, Francesco P. and Cools, Kristof (2017) A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Abstract-A discretization of the IBC-EFIE is introduced that (i) yields the correct solution at arbitrarily small frequencies, (ii) requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases. The low frequency stabilization is based on a projectorbased discrete Helmholtz splitting, rescaling, and recombination that depends on the low frequency behavior of both the EFIE operator and the surface impedance condition. The dense mesh stabilization is a modification of the perfect electric conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the IBC term.

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Novel Buffa-Christiansen Functions for Improving CFIE With Impedance Boundary Condition

Cited by 12 publications

References 21 publications

A Well-Posed and Effective High-Order Impedance Boundary Condition for the Time-Harmonic Scattering Problem From a Multilayer Coated 3-D Object

A Well-Posed and Effective High-Order Impedance Boundary Condition for the Time-Harmonic Scattering Problem From a Multilayer Coated 3-D Object

A Concise and Efficient MLFMA Scheme for Electromagnetic Surface Integral Equations From Dielectric Objects

An Impedance Boundary Condition EFIE That Is Low-Frequency and Refinement Stable

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