Evaluation of potential integral at singularity of exact kernel in thin-wire calculations

Butler, C.M.

doi:10.1109/tap.1975.1141028

Cited by 46 publications

(27 citation statements)

References 5 publications

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“…To solve this problem, much attention has gone to the development of numerical and semianalytical techniques to compute these impedance integrals. Among the most widely used techniques are the singularity subtraction [3][4][5][6] and singularity cancelation [7][8][9][10] techniques.…”

Section: Introductionmentioning

confidence: 99%

On the analytical treatment of singular impedance integrals in electromagnetics

Bogaert

2013

2013 International Conference on Electromagnetics in Advanced Applications (ICEAA)

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-A method is presented for reducing the number of subsequent integrations in impedance integrals containing the dynamic Green's function. The method works whenever a point can be found that is coplanar (or collinear) to both the basis and test support. This is always the case for singular impedance integrals. As an example, explicit formulas are given for the self-patch impedance integrals for the electric field integral equation.

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Section: Introductionmentioning

confidence: 99%

On the analytical treatment of singular impedance integrals in electromagnetics

Bogaert

2013

2013 International Conference on Electromagnetics in Advanced Applications (ICEAA)

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“…This technique can also be used for the dynamic Green's function, using a technique called singularity extraction [2][3][4]. A disadvantage of this technique is that F (r) can still have non-smooth features, such as the presence of singular derivatives for ν = −1 when V b and V t share a part of their support.…”

Section: Introductionmentioning

confidence: 99%

“…This scheme results in a wellcontrolled error, as opposed to when a direct product Gauss-Legendre quadrature rule would be used. Alternatively, a number of so-called singularity cancelation methods have been proposed [6][7][8][9] for the evaluation of (2), that avoid the need for analytical results and can be extended to basis functions with curvilinear support. It is clear that the methods mentioned above involve a trade-off between accuracy and speed.…”

Section: Introductionmentioning

confidence: 99%

Analytical computation of impedance integrals with power-law Green's functions

Bogaert

2012

2012 International Conference on Electromagnetics in Advanced Applications

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-In this contribution, a method is presented for reducing the number of subsequent integrations that occur in impedance integrals with Green's functions of the form R ν , with R the distance between source and observation point. The method allows the number of integrations to be reduced to 1 in the two dimensional case and 2 in the three dimensional case, irrespective of the number of subsequent integrations that were originally present. These last integrations can be done analytically using well-known results if ν ∈ Z, resulting in a computation that is free of numerical integrations. The dynamic Green's function can be treated in a semianalytical way, by expanding it into a Taylor series in the wavenumber. The method can be applied if both the basis and test functions are polynomial functions with polygonal support and if certain non-parallelity conditions are satisfied.

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“…T RADITIONALLY, the singularity present in the method of moments (MoM) analysis for wires has been evaluated analytically using singularity extraction techniques [1]- [3]. In the 1990s, an approach that avoids singularity extraction by exactly representing the wire kernel as an infinite series was proposed [4]- [6].…”

Section: Introductionmentioning

confidence: 99%

Evaluation and Integration of the Thin Wire Kernel

Wilton

Champagne

2006

IEEE Trans. Antennas Propagat.

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New approaches for numerically computing the thin wire kernel and wire potential integrals are presented. The singular behavior of the kernel integral is removed by transforming the integration variable to produce a smooth integrand. Subsequent integration of the kernel to obtain potential integrals uses quadrature schemes catering to its behavior. This technique allows standard algorithms for numerical quadrature to be used with updated integration weights that account for the transformed behavior, obviating the need for singularity subtraction techniques. The result is a procedure for evaluating the potential integrals that is independent of the basis functions.

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Evaluation of potential integral at singularity of exact kernel in thin-wire calculations

Cited by 46 publications

References 5 publications

On the analytical treatment of singular impedance integrals in electromagnetics

On the analytical treatment of singular impedance integrals in electromagnetics

Analytical computation of impedance integrals with power-law Green's functions

Evaluation and Integration of the Thin Wire Kernel

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