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   -> Volume 6, Issue 10

Preprint: Title: Integral Equations Using Wavelet Packets
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Hai Deng (

PostPosted: Fri Sep 12, 1997 7:47 pm    
Subject: Preprint: Title: Integral Equations Using Wavelet Packets
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#3 Preprint: Title: Integral Equations Using Wavelet Packets

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Title: Fast Solution of Electromagnetic Integral Equations Uing Adaptive
Wavelet Packet Transform

Authors: Hai Deng and Hao Ling

Department of Electrical and Computer Engineering
The University of Texas at Austin
Austin, TX 78712-1084

Abstract: The conventional wavelet transform (CWT) is widely used to
compress smooth operators. But it is not efficient for the compression
of some oscillatory operators, such as the Green function in
electromagnetic integral equations. In this paper we apply the
Adaptive Wavelet Packet Transform (AWPT) to the compression of moment
matrix, which is the discretized Green function, based on the
understanding that wavelet packet function is a modulated wavelet. A
cost function is employed to adaptively select the optimal wavelet
packet expansion/testing functions to achieve the maximum sparsity in
the transformed moment matrix. Numerical results show that the
thresheld elements in the AWPT transformed moment matrix grow only as
O(N^1.4) for typical scatterers. Consequently the solutions of the
transformed equations need only O(N^1.4) operations using recursive
methods such as Conjugate Gradient solver.

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