Weighted Averages and Double Exponential Algorithms

Juan R. MOSIG

doi:10.1587/transcom.E96.B.2355

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Weighted Averages and Double Exponential Algorithms

Juan R. MOSIG

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This paper reviews two simple numerical algorithms particularly useful in Computational ElectroMagnetics (CEM): the Weighted Averages (WA) algorithm and the Double Exponential (DE) quadrature. After a short historical introduction and an elementary description of the mathematical procedures underlying both techniques, they are applied to the evaluation of Sommerfeld integrals, where WA and DE combine together to provide a numerical tool of unprecedented quality. It is also shown that both algorithms have a much wider range of applications. A generalization of the WA algorithm, able to cope with integrands including products of Bessel and similar oscillatory functions, is described. Similarly, the original DE algorithm is adapted with exceptional results to the evaluation of the multidimensional singular integrals arising in the discretization of Integral-Equation based CEM formulations. The new possibilities of WA and DE algorithms are demonstrated through several practical numerical examples.

Publication: IEICE TRANSACTIONS on Communications Vol.E96-B No.10 pp.2355-2363

Publication Date: 2013/10/01

Publicized

Online ISSN: 1745-1345

DOI: 10.1587/transcom.E96.B.2355

Type of Manuscript: Special Section INVITED PAPER (Special Section on Recent Progress in Antennas and Propagation in Conjunction with Main Topics of ISAP2012)

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Authors

Juan R. MOSIG
Ecole Polytechnique F'{e}d'{e}rale de Lausanne (EPFL)

Keyword

weighted averages, double exponential, Sommerfeld integrals, multidimensional singular integrals, oscillatory functions

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Juan R. MOSIG, "Weighted Averages and Double Exponential Algorithms" in IEICE TRANSACTIONS on Communications, vol. E96-B, no. 10, pp. 2355-2363, October 2013, doi: 10.1587/transcom.E96.B.2355.
Abstract: This paper reviews two simple numerical algorithms particularly useful in Computational ElectroMagnetics (CEM): the Weighted Averages (WA) algorithm and the Double Exponential (DE) quadrature. After a short historical introduction and an elementary description of the mathematical procedures underlying both techniques, they are applied to the evaluation of Sommerfeld integrals, where WA and DE combine together to provide a numerical tool of unprecedented quality. It is also shown that both algorithms have a much wider range of applications. A generalization of the WA algorithm, able to cope with integrands including products of Bessel and similar oscillatory functions, is described. Similarly, the original DE algorithm is adapted with exceptional results to the evaluation of the multidimensional singular integrals arising in the discretization of Integral-Equation based CEM formulations. The new possibilities of WA and DE algorithms are demonstrated through several practical numerical examples.
URL: https://global.ieice.org/en_transactions/communications/10.1587/transcom.E96.B.2355/_p

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@ARTICLE{e96-b_10_2355,
author={Juan R. MOSIG, },
journal={IEICE TRANSACTIONS on Communications},
title={Weighted Averages and Double Exponential Algorithms},
year={2013},
volume={E96-B},
number={10},
pages={2355-2363},
abstract={This paper reviews two simple numerical algorithms particularly useful in Computational ElectroMagnetics (CEM): the Weighted Averages (WA) algorithm and the Double Exponential (DE) quadrature. After a short historical introduction and an elementary description of the mathematical procedures underlying both techniques, they are applied to the evaluation of Sommerfeld integrals, where WA and DE combine together to provide a numerical tool of unprecedented quality. It is also shown that both algorithms have a much wider range of applications. A generalization of the WA algorithm, able to cope with integrands including products of Bessel and similar oscillatory functions, is described. Similarly, the original DE algorithm is adapted with exceptional results to the evaluation of the multidimensional singular integrals arising in the discretization of Integral-Equation based CEM formulations. The new possibilities of WA and DE algorithms are demonstrated through several practical numerical examples.},
keywords={},
doi={10.1587/transcom.E96.B.2355},
ISSN={1745-1345},
month={October},}

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TY - JOUR
TI - Weighted Averages and Double Exponential Algorithms
T2 - IEICE TRANSACTIONS on Communications
SP - 2355
EP - 2363
AU - Juan R. MOSIG
PY - 2013
DO - 10.1587/transcom.E96.B.2355
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E96-B
IS - 10
JA - IEICE TRANSACTIONS on Communications
Y1 - October 2013
AB - This paper reviews two simple numerical algorithms particularly useful in Computational ElectroMagnetics (CEM): the Weighted Averages (WA) algorithm and the Double Exponential (DE) quadrature. After a short historical introduction and an elementary description of the mathematical procedures underlying both techniques, they are applied to the evaluation of Sommerfeld integrals, where WA and DE combine together to provide a numerical tool of unprecedented quality. It is also shown that both algorithms have a much wider range of applications. A generalization of the WA algorithm, able to cope with integrands including products of Bessel and similar oscillatory functions, is described. Similarly, the original DE algorithm is adapted with exceptional results to the evaluation of the multidimensional singular integrals arising in the discretization of Integral-Equation based CEM formulations. The new possibilities of WA and DE algorithms are demonstrated through several practical numerical examples.
ER -