Accuracy of the method of moments for scattering by a cylinder

Warnick, K.E.; Chew, Weng Cho

doi:10.1109/22.873892

Cited by 38 publications

(23 citation statements)

References 12 publications

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“…It is obvious that (23) compares very well with the exact expression (22), even for moderate values of the scatterer radius b. Like in [10], resonance effects are not taken into account in (23), implying that (23) yields only a lower bound of the condition number [10,11]. However, the spikes due to the resonance effects are extremely narrow, and hence practically invisible in the analytical plots of Fig.…”

Section: Numerical Results and Discussionmentioning

confidence: 62%

“…It is worth mentioning that this phenomenon is observed for both polarizations; the resonance points of the TE polarization are also related to the zeros of the Bessel function itself, and not its derivative, as may be expected a priori. This is due to the fact that the AS's were defined as magnetic, and not electric elementary currents in the analysis of the TE case, which is analogous to a MFIE (and not EFIE) MoM approach [11].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…For the circular cylinder case, (6) can be solved analytically, via diagonalization and subsequent inversion of [Z], i.e., via a procedure described in detail in [9,10]. The eigenvalues and eigenvectors of [Z] are evaluated according to a method described in [11], adapted to the present problem. Alternatively, since [Z] is circulant, the procedure described in Appendix B can be utilized.…”

Section: Analytical Considerations (Tm Polarization)mentioning

confidence: 99%

“…It was shown that for this particular geometry, the MAS matrix is prone to analytical inversion, via spectral analysis and matrix diagonalization, on the basis of a technique described in [11,12]. The analysis facilitated the derivation of an exact expression for the boundary condition discretization error, as well as for the system condition number.…”

Section: Introductionmentioning

confidence: 99%

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Error Estimation of the Method of Auxiliary Sources (Mas) for Scattering From an Impedance Circular Cylinder

Anastassiu¹

2005

PIER

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Abstract-The purpose of this paper is a rigorous error estimation of the Method of Auxiliary Sources (MAS), when the latter is applied to electromagnetic scattering from a circular, coated, perfectly conducting cylinder, assumed to satisfy the Standard Impedance Boundary Condition (SIBC). The MAS matrix is inverted analytically, via eigenvalue analysis, and an exact expression for the discretization error in the boundary condition is derived. Furthermore, an analytical formula for the condition number of the linear system is also extracted, in addition to an asymptotic estimate for large scatterers, explaining the irregular behavior of the computational error resulting from numerical matrix inversion. Finally, the optimal location of the auxiliary sources is determined, on the grounds of error minimization.

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Section: Numerical Results and Discussionmentioning

confidence: 62%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Analytical Considerations (Tm Polarization)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Error Estimation of the Method of Auxiliary Sources (Mas) for Scattering From an Impedance Circular Cylinder

Anastassiu¹

2005

PIER

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“…On the other hand, MFIE has better convergence rate when solved with an iterative solver [1,2]. Also, EFIE has low-frequency breakdown, but MFIE does not have an apparent low-frequency problem [3].We will perform error analysis to explain why EFIE has better accuracy compared to MFIE [4][5][6][7]. Mathematical analysis shows that EFIE has a smoothing operator, while MFIE has a non-smoothing operator [8][9][10].…”

mentioning

confidence: 99%

EFIE and MFIE, why the difference?

Chew¹,

Davis

Warnick

et al. 2008

2008 IEEE Antennas and Propagation Society International Symposium

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EFIE (electric field integral equation) suffers from internal resonance, and the remedy is to use MFIE (magnetic field integral equation) to come up with a CFIE (combined field integral equation) to remove the internal resonance problem. However, MFIE is fundamentally a very different integral equation from EFIE. Many questions have been raised about the differences.First, it has often been observed that EFIE has better accuracy than MFIE. On the other hand, MFIE has better convergence rate when solved with an iterative solver [1,2]. Also, EFIE has low-frequency breakdown, but MFIE does not have an apparent low-frequency problem [3].We will perform error analysis to explain why EFIE has better accuracy compared to MFIE [4][5][6][7]. Mathematical analysis shows that EFIE has a smoothing operator, while MFIE has a non-smoothing operator [8][9][10]. This difference often gives rise to better accuracy for EFIE compared to MFIE.MFIE is a second kind integral equation while EFIE is a first kind integral equation [10]. Hence, the eigenvalues of the EFIE operator tends to cluster around the origin, while the eigenvalues of the MFIE operator are shifted away from the origin. Consequently, when solved with an iterative solver, the convergence behavior of MFIE is superior to that of EFIE.It is well-known that EFIE suffers from the low-frequency breakdown problem. MFIE does not suffer from apparent low-frequency breakdown, but it suffers from low-frequency inaccuracy [3]. All these problems can be taken care of by performing the loop-tree decomposition.The EFIE operator is often known as the L operator and the MFIE operator is often known as the K operator in the literature. The L operator is a symmetric operator while the K operator is an asymmetric operator. In some integral equations such as those involving dielectric interfaces, these two operators appear simultaneously. They also appear concurrently in the invocation of the equivalence principle. Their discretization often gives rise 978-1-4244-2042-1/08/$25.00 ©2008 IEEE

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Richie

2018

The Generalized Multipole Technique for Light Scattering

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Accuracy of the method of moments for scattering by a cylinder

Cited by 38 publications

References 12 publications

Error Estimation of the Method of Auxiliary Sources (Mas) for Scattering From an Impedance Circular Cylinder

Error Estimation of the Method of Auxiliary Sources (Mas) for Scattering From an Impedance Circular Cylinder

EFIE and MFIE, why the difference?

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