Application of Wavelets to Scattering Problems of Inhomogeneous Dielectric Slabs

Jeng-Long LEOU; Jiunn-Ming HUANG; Shyh-Kang JENG; Hsueh-Jyh LI

Application of Wavelets to Scattering Problems of Inhomogeneous Dielectric Slabs

Jeng-Long LEOU, Jiunn-Ming HUANG, Shyh-Kang JENG, Hsueh-Jyh LI

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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.

Publication: IEICE TRANSACTIONS on Communications Vol.E82-B No.10 pp.1667-1676

Publication Date: 1999/10/25

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Type of Manuscript: PAPER

Category: Electronic and Radio Applications

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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 -