On Application of Fast and Adaptive Periodic Battle–Lemarie Wavelets to Modeling of Multiple Lossy Transmission Lines
✍ Scribed by Xiaojun Zhu; Guangtsai Lei; Guangwen Pan
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 492 KB
- Volume
- 132
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
The wavelet expansion has proven to be an efficient method in the approximation of functions [2][3][4][5], thus pro-In this paper, the continuous operator is discretized into matrix forms by Galerkin's procedure, using periodic Battle-Lemarie waveviding an effective approach to the solution of integral lets as basis/testing functions. The polynomial decomposition of equations. Because of the localized property, vanishing wavelets is applied to the evaluation of matrix elements, which moment, and multiresolution analysis (MRA) of the wavemakes the computational effort of the matrix elements no more lets, the resolution level of the solution, which is closely expensive than that of method of moments (MoM) with convenrelated to the grid size and the length of the wavelet series, tional piecewise basis/testing functions. A new algorithm is developed employing the fast wavelet transform (FWT). Owing to localizacan be chosen adaptively, according to the smoothness of tion, cancellation, and orthogonal properties of wavelets, very the function at different locations. Beylkin et al. [6] first sparse matrices have been obtained, which are then solved by the proposed a nonstandard form wavelet expansion of opera-LSQR iterative method. This algorithm is also adaptive in that one tors by projecting the operator onto a series of subspaces.
can add at will finer wavelet bases in the regions where fields vary rapidly, without any damage to the system orthogonality of the Wavelets were employed as basis functions in the MoM wavelet basis functions. To demonstrate the effectiveness of the (method of moments) [7][8][9][10].
new algorithm, we applied it to the evaluation of frequency-depen-Since in most practical problems the unknowns are dedent resistance and inductance matrices of multiple lossy transmisfined on a finite domain, while most orthonormal wavelets sion lines. Numerical results agree with previously published data are developed in L 2 (ᑬ), it is very inefficient to employ and laboratory measurements. The valid frequency range of the boundary integral equation results has been extended two to three these wavelets as bases directly. To overcome this diffidecades in comparison with the traditional MoM approach. The culty, the periodic wavelets [11,12], intervallic wavelets new algorithm has been integrated into the computer aided design [13], and weighted wavelets [14] are applied to practical tool, MagiCAD, which is used for the design and simulation of highelectromagnetic problems. speed digital systems and multichip modules Pan et al. IEEE Trans.