Wavelet-based multiresolution algorithm for integral and boundary element equations in electric and magnetic field computations

Summary form only given. The wavelet algorithm for integral equations was first studied by Beylkin et al.(1991). When applied to electric and magnetic field problems formulated in terms of the method of moments (MoM) or the boundary element method (BEM), it was recognized that the wavelet transform (WT) yielded a sparse algebraic equation matrix. However, when the domain was discretized with regular basis functions, for example piecewise constant or piecewise linear, it was necessary to allocate extra memory for the transformed matrix. Moreover, the transformed matrix did not appear to have a better condition number than that of the original one. We use wavelet functions as both basis and weight functions to obtain a reasonable trade-off between the entire domain and subsectional basis functions. The whole domain may be divided into several subsections. In each subsection, the higher resolution basis is incorporated, thus preserving the merits of entire domain basis functions while yielding a sparse matrix. The wavelet-based multiresolution algorithm is described in the full paper and numerical examples are presented to illustrate its flexibility.