Abstract
In this paper, wavelets transformation (WT) and wavelet packet transformation (WPT) are used in solving, by the method of moments, a semicircular array of parallel wires electric field integral equation. First, the integral equation is solved by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix. Therefore, wavelet transformation and wavelet packet transformation are used to sparsify the impedance matrix, using two categories of wavelets functions, Biorthogonal (bior2.2) and Orthogonal (db4) wavelets. The far-field scattering patterns and the comparison between wavelets transformation and wavelet packet transformation in term number of zeros in impedance matrix and CPU Time reduction are presented. Numerical results are presented to identify which technique is best suited to solve such scattering electromagnetic problems and compared with published results.
Highlights
The art of computation of electromagnetic (EM) problems has grown exponentially for three decades due to the availability of powerful computer resources
The above theory was implemented has been coded in Matlab language for calculating the induced current, and scattering pattern of the an Arbitrary Array of Parallel Wires and comparison of three methods, MoM, MoM/wavelets transformation (WT), and MoM/wavelet packet transformation (WPT), in terms of Sparsity of impedance matrix (IM) and CPU Time to reverse IM
The plots of Scattering pattern E(φ) against φ for array of parallel wire are portrayed in Figs. 4.a and 4.b for the Daubechies and Biorthogonal wavelets, respectively
Summary
The art of computation of electromagnetic (EM) problems has grown exponentially for three decades due to the availability of powerful computer resources. Wavelet packet bases are designed by dividing the frequency axis in intervals of varying sizes. The wavelets are a powerful technique for solving integral equations, resulting in sparse impedance matrices [1]. This is due to features of vanishing moments, orthogonality and multiresolution analysis in wavelets. The wavelet approach is used directly on the impedance matrix in order to make it sparse rather than on the operator equations in the form of a set of basis functions to approximate the unknown. The last section contains conclusions and suggestions for future research
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