The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dans cet article, nous appliquons la transformée en ondelettes discrète (DWT) et la transformée en paquets d'ondelettes discrète (DWPT) avec l'ondelette de Daubechies d'ordre 16 pour résoudre efficacement la diffusion électromagnétique à partir d'une dalle inhomogène unidimensionnelle. Méthodes basées sur le vecteur d'excitation et le [Z] sont utilisés pour sparsifier une matrice MoM. Comme nous l'avons observé, il n'y a pas beaucoup de composantes haute fréquence du champ dans la région diélectrique, donc les coefficients d'ondelette des composantes à petite échelle (composantes haute fréquence) sont très faibles et négligeables. Ceci est différent du cas de la diffusion bidimensionnelle à partir d’objets parfaitement conducteurs. Dans la méthode basée sur le vecteur d'excitation, un vecteur d'excitation modifié est introduit pour extraire les termes dominants et obtenir un meilleur taux de compression de la matrice. Cependant, un taux de compression plus faible et une erreur relative minime ne sont pas obtenus simultanément en raison de la suppression de l'interaction entre les différentes échelles. Il est donc inférieur au [Z]-méthodes basées sur une matrice. Pour le [Z]-marix, nos résultats numériques montrent que la méthode DWPT basée sur l'arborescence des colonnes est un meilleur choix pour fragmenter la matrice MoM que les méthodes basées sur DWT et d'autres méthodes basées sur DWPT. Le coût d’une multiplication matrice-vecteur pour la matrice clairsemée à domaine d’ondelettes est réduit d’un facteur 10 par rapport à celui de la matrice dense d’origine.
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Jeng-Long LEOU, Jiunn-Ming HUANG, Shyh-Kang JENG, Hsueh-Jyh LI, "Application of Wavelets to Scattering Problems of Inhomogeneous Dielectric Slabs" in IEICE TRANSACTIONS on Communications,
vol. E82-B, no. 10, pp. 1667-1676, October 1999, doi: .
Abstract: In this paper, we apply the discrete wavelet transform (DWT) and the discrete wavelet packet transform (DWPT) with the Daubechies wavelet of order 16 to effectively solve for the electromagnetic scattering from a one-dimensional inhomogeneous slab. Methods based on the excitation vector and the [Z] matrix are utilized to sparsify an MoM matrix. As we observed, there are no much high frequency components of the field in the dielectric region, hence the wavelet coefficients of the small scales components (high frequency components) are very small and negligible. This is different from the case of two-dimensional scattering from perfect conducting objects. In the excitation-vector-based method, a modified excitation vector is introduced to extract dominant terms and achieve a better compression ratio of the matrix. However, a smaller compression ratio and a tiny relative error are not obtained simultaneously owing to their deletion of interaction between different scales. Hence, it is inferior to the [Z]-matrix-based methods. For the [Z]-marix-based methods, our numerical results show the column-tree-based DWPT method is a better choice to sparsify the MoM matrix than DWT-based and other DWPT-based methods. The cost of a matrix-vector multiplication for the wavelet-domain sparse matrix is reduced by a factor of 10, compared with that of the original dense matrix.
URL: https://global.ieice.org/en_transactions/communications/10.1587/e82-b_10_1667/_p
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@ARTICLE{e82-b_10_1667,
author={Jeng-Long LEOU, Jiunn-Ming HUANG, Shyh-Kang JENG, Hsueh-Jyh LI, },
journal={IEICE TRANSACTIONS on Communications},
title={Application of Wavelets to Scattering Problems of Inhomogeneous Dielectric Slabs},
year={1999},
volume={E82-B},
number={10},
pages={1667-1676},
abstract={In this paper, we apply the discrete wavelet transform (DWT) and the discrete wavelet packet transform (DWPT) with the Daubechies wavelet of order 16 to effectively solve for the electromagnetic scattering from a one-dimensional inhomogeneous slab. Methods based on the excitation vector and the [Z] matrix are utilized to sparsify an MoM matrix. As we observed, there are no much high frequency components of the field in the dielectric region, hence the wavelet coefficients of the small scales components (high frequency components) are very small and negligible. This is different from the case of two-dimensional scattering from perfect conducting objects. In the excitation-vector-based method, a modified excitation vector is introduced to extract dominant terms and achieve a better compression ratio of the matrix. However, a smaller compression ratio and a tiny relative error are not obtained simultaneously owing to their deletion of interaction between different scales. Hence, it is inferior to the [Z]-matrix-based methods. For the [Z]-marix-based methods, our numerical results show the column-tree-based DWPT method is a better choice to sparsify the MoM matrix than DWT-based and other DWPT-based methods. The cost of a matrix-vector multiplication for the wavelet-domain sparse matrix is reduced by a factor of 10, compared with that of the original dense matrix.},
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - Application of Wavelets to Scattering Problems of Inhomogeneous Dielectric Slabs
T2 - IEICE TRANSACTIONS on Communications
SP - 1667
EP - 1676
AU - Jeng-Long LEOU
AU - Jiunn-Ming HUANG
AU - Shyh-Kang JENG
AU - Hsueh-Jyh LI
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Communications
SN -
VL - E82-B
IS - 10
JA - IEICE TRANSACTIONS on Communications
Y1 - October 1999
AB - In this paper, we apply the discrete wavelet transform (DWT) and the discrete wavelet packet transform (DWPT) with the Daubechies wavelet of order 16 to effectively solve for the electromagnetic scattering from a one-dimensional inhomogeneous slab. Methods based on the excitation vector and the [Z] matrix are utilized to sparsify an MoM matrix. As we observed, there are no much high frequency components of the field in the dielectric region, hence the wavelet coefficients of the small scales components (high frequency components) are very small and negligible. This is different from the case of two-dimensional scattering from perfect conducting objects. In the excitation-vector-based method, a modified excitation vector is introduced to extract dominant terms and achieve a better compression ratio of the matrix. However, a smaller compression ratio and a tiny relative error are not obtained simultaneously owing to their deletion of interaction between different scales. Hence, it is inferior to the [Z]-matrix-based methods. For the [Z]-marix-based methods, our numerical results show the column-tree-based DWPT method is a better choice to sparsify the MoM matrix than DWT-based and other DWPT-based methods. The cost of a matrix-vector multiplication for the wavelet-domain sparse matrix is reduced by a factor of 10, compared with that of the original dense matrix.
ER -