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

Accurate integration of singular and near-singular functions is critical to the accuracy of the method of moments solution to surface integral equations. While this problem has been widely addressed for flat geometries, its extensions to higher order surface descriptions have been limited. This lett...

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Bibliographic Details
Published inIEEE transactions on antennas and propagation Vol. 61; no. 4; pp. 2347 - 2352
Main Authors Nair, N. V., Pray, A. J., Villa-Giron, J., Shanker, B., Wilton, D. R.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.04.2013
Institute of Electrical and Electronics Engineers
Subjects
Accuracy
Convergence
Educational institutions
Exact sciences and technology
Geometry
Integral equations, integral transforms
Jacobian matrices
Mathematics
Near singularity
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Polynomials
Sciences and techniques of general use
singular quadrature
singularity cancellation
Surface treatment
Letter
Quadrature
Singularity
singular quadrature
Moment method
Boundary integral method
Near singularity
singularity cancellation
Integral equation
Non linear effect
Modeling
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Summary:Accurate integration of singular and near-singular functions is critical to the accuracy of the method of moments solution to surface integral equations. While this problem has been widely addressed for flat geometries, its extensions to higher order surface descriptions have been limited. This letter provides a systematic prescription for the application of the rules for weakly singular integrals on higher order surfaces. Here, we present implementation details and several demonstrative results that compare the accuracy and convergence of the integration rules.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2013.2238880