An adaptive wavelet transform for solutions of electromagnetic integral equations

A multiresolution study is proposed for effective solutions of electromagnetic integral equations. The circular wavelet matrix is developed by a fast iterative algorithm from the conventional multiresolution analysis of L/sup 2/(R). Sparse matrix equations can be obtained by using the proposed wavelet transform method. The so-called "edge effect" and exhaustive wavelet integrations in the wavelet expansion method are avoided. An adaptive discretization scheme is proposed and found more effective than the conventional equal-space discretization scheme. For large-size EM problems whose integral boundaries are characterized by a variety of radii of curvatures ranging from several wavelengths to a small level-scale compared with the wavelength the proposed method shows a obvious advantage over other traditional methods. Numerical results are given to show the validity and effectiveness of the method.