DIRECTFN: Fully Numerical Algorithms for High Precision Computation of Singular Integrals in Galerkin SIE Methods

Fully numerical schemes are presented for high precision computations of the four-dimensional integrals arising in Galerkin surface integral equation formulations. More specifically, the focal point of this paper is the singular integrals for coincident, edge adjacent and vertex adjacent planar and...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2013-06, Vol.61 (6), p.3112-3122
Main Authors: Polimeridis, Athanasios G., Vipiana, F., Mosig, J. R., Wilton, D. R.
Format: Article
Language:English
Subjects:
Applied classical electromagnetism
Applied sciences
Diffraction, scattering, reflection
Electric potential
Electromagnetic scattering
Electromagnetic wave propagation, radiowave propagation
Electromagnetism
electron and ion optics
Exact sciences and technology
Frequency modulation
Fundamental areas of phenomenology (including applications)
Integral equations
Jacobian matrices
Kernel
method of moments (MoM)
Moment methods
numerical analysis
Physics
Radiocommunications
Radiowave propagation
singular integrals
surface integral equations
Telecommunications
Telecommunications and information theory
Testing
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Summary:Fully numerical schemes are presented for high precision computations of the four-dimensional integrals arising in Galerkin surface integral equation formulations. More specifically, the focal point of this paper is the singular integrals for coincident, edge adjacent and vertex adjacent planar and curvilinear triangular elements. The proposed method, dubbed as DIRECTFN, utilizes a series of variable transformations, able to cancel both weak (1/ R ) and strong (1/ R 2 ) singularities. In addition, appropriate interchanges in the order of the associated one-dimensional integrations result in further regularization of the overall integrals. The final integrands are analytic functions with respect to all variables involved and, hence, the integrals can be efficiently evaluated by means of simple Gaussian integration. The accuracy and convergence properties of the new schemes are demonstrated by evaluating representative weakly singular and strongly singular integrals over planar and quadratic curvilinear elements.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2013.2246854