Computable error bounds for variational functionals of solutions of a convolution integral equations of the first kind

Kuester, Edward F.

doi:10.1016/0165-2125(95)00020-j

Cited by 8 publications

(1 citation statement)

References 46 publications

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“…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.…”

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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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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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On the spectrum of the electric field integral equation and the convergence of the moment method

Warnick,

Chew

2001

Numerical Meth Engineering

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Existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self‐coupling of surface wave modes, the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations. From the spectrum of the EFIE, the solution error introduced by discretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discretization length for low‐order bases with exact integration of matrix elements, and is first order if an approximate quadrature rule is employed. Comparison with numerical results demonstrates the validity of these condition number and solution error estimates. The spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics. Copyright © 2001 John Wiley & Sons, Ltd.

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Accuracy of the method of moments for scattering by a cylinder

Warnick

Chew

2000

IEEE Trans. Microwave Theory Techn.

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Computable error bounds for variational functionals of solutions of a convolution integral equations of the first kind

Cited by 8 publications

References 46 publications

EFIE and MFIE, why the difference?

EFIE and MFIE, why the difference?

On the spectrum of the electric field integral equation and the convergence of the moment method

Accuracy of the method of moments for scattering by a cylinder

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