A Singularity Cancellation Technique for Weakly Singular Integrals on Higher Order Surface Descriptions

Nair, N. V.; Pray, A. J.; Villa-Giron, J.; Shanker, B.; Wilton, Donald R.

doi:10.1109/tap.2013.2238880

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…A number of schemes have been developed to handle the near singularity on flat triangle elements [3]- [12], whereas the literature about the near singularity on curved triangles or curved quadrilaterals is scarce [13], [14]. Obviously, the schemes for curved elements are much more difficult than that for flat elements, and the former is not a ready extension of the latter.…”

Section: Introductionmentioning

confidence: 99%

“…When the source element coincides with the observation element, there is a 1/R singularity in the integrand of the inner surface integral, which is often handled by singularity subtraction methods for flat triangle elements [3], [14], or variable transformations for curved elements [15]- [17]. Although these transformations are suitable for the singularity when the observation point is right on the source element, they are not suitable for the near singularity when the observation point is just very close to the source element.…”

Section: Introductionmentioning

confidence: 99%

“…However, from the point of views of numerical integrations, the inner integrands are peak-like functions and the standard integration quadratures fail in accuracy. The techniques to handle these near singularities can also be classified into the singularity subtraction schemes [3]- [7] and singularity cancellation schemes [8]- [14]. In the singularity subtraction methods, a singular term with the same asymptotic behavior as the integrand at the singularities is subtracted out and evaluated analytically.…”

Section: Introductionmentioning

confidence: 99%

“…Reference [14] advised to project the observation point onto the curved triangle, then find the tangential plane through this projection point, and then map the curved triangle onto this plane, and use a sin h −1 or polar coordinate transformation to evaluate the inner nearsingular surface integral numerically. This method may be very slow, because the projection point has to be found by numerical methods.…”

Section: Introductionmentioning

confidence: 99%

“…Transmit-arrays, wherein the elements are connected through multiple layers by a delay line, introduce losses to the structure and thus degrade the gain of the transmit-array [10]- [13]. Multiple layer transmit-arrays have also been reported [14], [15], the unit-cells are configured by multiple layers separated by air gaps which introduce certain phase…”

Section: Introductionmentioning

confidence: 99%

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A Simple Transformation for Near-Singular Integrals on Curvilinear Elements

Yuan

Wang

Dang

et al. 2015

IEEE Trans. Antennas Propagat.

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at 5.3, and the values of θ1 and θ2 are adjusted in relation to (3). The results show that the pattern null width is reduced by the increased aperture radius; however, the pattern null depth tends to be increased as the aperture size becomes larger. Thus, the optimum aperture radius can be found within the range 9-10 cm, which includes the optimum array radius of the proposed array configuration. IV. CONCLUSIONWe have investigated the curved array split into two subarrays to improve the null steering performance for CRPA systems. The proposed array is composed of a single reference element at the center and two subarrays that are placed on the spherical curvature. Both signal processing and EM perspectives were taken into account by calculating array patterns using a microstrip patch antenna in conjunction with the constraint LMS algorithm. The optimum element positions, array radius, and array curvature were found by optimizing the pattern null depth and width, and the suitability of the proposed array was evaluated by comparing its null steering performance with the UCA configuration. The results demonstrated that the pattern null depth and width of the proposed array were improved by 4.8 dB and 58.6 • , respectively, for low-elevation interference sources. REFERENCES [1] M. beam steering/null steering algorithm for CW interference mitigation in GPS C/A code receivers," IEEE Trans.Abstract-It is difficult to evaluate the near-singular four-dimensional integrals in the Galerkin magnetic-field integral equations (MFIE), especially for the curvilinear elements. This communication presents a hyperbolic transformation to cancel the near singularities in the 1/R 2 kernel on curved quadrilateral elements, which is addressed theoretically and numerically. This method has a much simpler formula than the so-called DIRECTFN method, and its convergence rate may be much faster than the latter. This is demonstrated by evaluating the near-singular integral of a sharp-edged structure composed of two curvilinear quadrilaterals.Index Terms-Curvilinear quadrilateral, magnetic-field integral equation (MFIE), near singularity, transformation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Simple Transformation for Near-Singular Integrals on Curvilinear Elements

Yuan

Wang

Dang

et al. 2015

IEEE Trans. Antennas Propagat.

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Method of Moments: As Applied to the Solution of Electromagnetic Integral Equations

Dault

Shanker

2015

Wiley Encyclopedia of Electrical and Electronics Engineering

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Integral equation‐based techniques are one of the primary solution approaches for analysis of electromagnetic systems. Most electromagnetic integral equations cannot be solved analytically, and numerical methods are therefore required. The most common numerical solution technique for these types of equations is the moment method. Over the past few decades, several bottlenecks in terms of accuracy and cost of the moment method have been solved, so much so that analysis of problems in excess of millions of degrees of freedom is now almost routine. Given the ubiquity of these numerical methods, and because the moment method and the formulation of integral equations are inextricably linked, this article presents a gentle introduction to some common classes of electromagnetic integral equations and accompanying moment method formulations to numerically solve them. Recent progress and unsolved and open problems in moment methods are also presented.

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Integration of the modified double layer potential of the vector boundary element method for eddy current problems

et al. 2022

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The boundary element method for the eddy current problem (BEM-ECP) was proposed in a number of papers and is applicable to important tasks such as the problem of inductive heating and transmission of electromagnetic energy. BEM-ECP requires the construction of a system of linear algebraic equations in which the matrix is inherently dense and is constructed out of element matrices. For the process of the element matrix computation, two cases are normally considered: far-field interaction and near-field interaction, because the construction of element matrices requires integration of a singular function. In this article, we suggest a transform that allows computing the matrix components of the near-singular interaction part while implementing only the single and double layer potentials. The previously suggested modified double layer potential (MDLP) can be integrated by means of this transform, which simplifies the program implementation of BEM-ECP significantly. Solving model problems, we analyse the drawbacks of the previously suggested approach. This analysis includes the proof of the MDLP singularity that makes the integration of this potential a rather difficult task without the help of our transform. The previously suggested approach does not work well with surfaces that are not smooth. Our approach does consider such cases, which is its main advantage. We demonstrate this on the model problems with known analytical solutions.

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A Singularity Cancellation Technique for Weakly Singular Integrals on Higher Order Surface Descriptions

Cited by 7 publications

References 24 publications

A Simple Transformation for Near-Singular Integrals on Curvilinear Elements

A Simple Transformation for Near-Singular Integrals on Curvilinear Elements

Method of Moments: As Applied to the Solution of Electromagnetic Integral Equations

Integration of the modified double layer potential of the vector boundary element method for eddy current problems

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