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

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

Polimeridis, Athanasios G.
•
Vipiana, Francesca
•
Mosig, Juan R.  
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2013
IEEE Transactions on Antennas and Propagation

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/R2) 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.

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Type
research article
DOI
10.1109/TAP.2013.2246854
Web of Science ID

WOS:000319871400027

Author(s)
Polimeridis, Athanasios G.
•
Vipiana, Francesca
•
Mosig, Juan R.  
•
Wilton, Donald R.
Date Issued

2013

Publisher

Institute of Electrical and Electronics Engineers

Published in
IEEE Transactions on Antennas and Propagation
Volume

61

Issue

6

Start page

3112

End page

3122

Subjects

Electromagnetic scattering

•

method of moments

•

numerical analysis

•

singular integrals

•

surface integral equations

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LEMA  
Available on Infoscience
September 7, 2012
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/85302
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