On the semi-orthogonal wavelet matrix transform approach for the solution of integral equations

In this paper, the semi-orthogonal wavelet (SOW) and Daubechies orthogonal wavelet (DOW) transforms have been applied to the solution of integral equations arising from the scattering by a conducting cylinder excited by a TM plane wave, and the effect of thresholding on the matrix sparsity and the solution accuracy has been examined for the entire practical range of matrix sparsity. Numerical results show that, although the computational costs of the SOW and the DOW matrix transformations are practically the same, the SOW matrix transform approach yields a highly sparse MoM matrix with a much smaller threshold value, and gives a better solution accuracy than the DOW matrix transform approach when the matrix sparsity is less than a certain value. However, the relative error /spl epsiv/ increases irregularly with the increase of the matrix sparsity when using the SOW, which indicates a worse transform matrix condition number in this case.