Considerations on double exponential-based cubatures for the computation of weakly singular Galerkin inner products

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

doi:10.1109/TAP.2012.2189708

Considerations on double exponential-based cubatures for the computation of weakly singular Galerkin inner products

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

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

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.

Original language	English
Article number	6163367
Journal	IEEE Transactions on Antennas and Propagation
Volume	60
Issue number	5
Pages (from-to)	2579-2582
Number of pages	4
ISSN	0018-926X
DOIs	https://doi.org/10.1109/TAP.2012.2189708
Publication status	Published - 2012
Externally published	Yes

Keywords

Double exponential quadrature
method of moments (MoM)
mixed potential integral equation (MPIE)
RWG basis functions
weakly singular integrals

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title = "Considerations on double exponential-based cubatures for the computation of weakly singular Galerkin inner products",

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.",

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author = "Polimeridis, {Athanasios G.} and Koufogiannis, {Ioannis D.} and Michael Mattes and Mosig, {Juan R.}",

year = "2012",

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pages = "2579--2582",

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Considerations on double exponential-based cubatures for the computation of weakly singular Galerkin inner products. / Polimeridis, Athanasios G.; Koufogiannis, Ioannis D.; Mattes, Michael; Mosig, Juan R.

In: IEEE Transactions on Antennas and Propagation, Vol. 60, No. 5, 6163367, 2012, p. 2579-2582.

Research output: Contribution to journal › Journal article › Research › peer-review

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T1 - Considerations on double exponential-based cubatures for the computation of weakly singular Galerkin inner products

AU - Polimeridis, Athanasios G.

AU - Koufogiannis, Ioannis D.

AU - Mattes, Michael

AU - Mosig, Juan R.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Double exponential quadrature

KW - method of moments (MoM)

KW - mixed potential integral equation (MPIE)

KW - RWG basis functions

KW - weakly singular integrals

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Considerations on double exponential-based cubatures for the computation of weakly singular Galerkin inner products

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