Considerations on Double Exponential-Based Cubatures for the Computation of Weakly Singular Galerkin Inner Products

Author

Polimeridis, Athanasios G. ; Koufogiannis, Ioannis D. ; Mattes, Michael ; Mosig, Juan R.

Author_Institution

Lab. of Electromagn. & Acoust. (LEMA), Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland

Volume

60

Issue

5

fYear

2012

fDate

5/1/2012 12:00:00 AM

Firstpage

2579

Lastpage

2582

Abstract

Highly accurate and efficient cubatures based on the double exponential quadrature rules are presented for the computation of weakly singular integrals arising in Galerkin mixed potential integral equation formulations. Due to their unique ability to handle non-smooth kernels, the proposed integration schemes can safely replace (in a “plug-n-play” sense) the traditional Gauss-Legendre rules in the existing singularity cancellation and singularity subtraction methods. Numerical examples using RWG basis functions confirm the excellent performance of the proposed method.

Keywords

Galerkin method; computational electromagnetics; electromagnetic wave scattering; integral equations; Gauss-Legendre rules; RWG basis functions; double exponential based cubatures; double exponential quadrature rules; integral equation formulations; nonsmooth kernels; singularity cancellation; singularity subtraction; weakly singular Galerkin inner products; Accuracy; Antennas; Electric potential; Electromagnetic scattering; Integral equations; Kernel; Moment methods; Double exponential quadrature; RWG basis functions; method of moments (MoM); mixed potential integral equation (MPIE); weakly singular integrals;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/TAP.2012.2189708

Filename

6163367