An efficient wavelet-based solution of electromagnetic field problems

This work investigates the applicability of wavelet transform in electromagnetic field problems. A new approach to the numerical solution of the electric field integral equation (EFIE) is proposed. Rather than applying wavelet bases directly to obtain new discretizations, we exploit the available wavelet bases to obtain more efficient solution algorithms for the classical discretizations. We discretize the EFIE using the method of moments (MoM). The discrete wavelet transform (DWT) is then applied to the resulting dense algebraic system. This procedure involves O(N2) operations and leads to a sparse matrix problem. Solving this sparse matrix system by iterative methods requires only O(Nlog2N) operations whereas O(N3) operations are required for the traditional methods. Comparisons of the run-times, number of iterations and error estimations are made for different iterative methods and for different sizes of the matrix equations. The advantages and shortcomings of the presented methods are discussed and the best choices are singled out.