Wavelet transform approach on boundary element method for solving electromagnetic scattering problems

We apply the wavelet transform approach to the boundary element method (BEM) for solving the electromagnetic scattering from conducting/dielectric cylinders with arbitrary cross sections. The problem is first reduced to a matrix equation by the BEM. Then the equation is transformed by the wavelet transform to produce a sparse matrix equation. Finally, the sparse equation is solved effectively by a sparse linear system solver. In order to preserve the condition number of the matrix and save the computation cost in the transform, the Daubechies' (1988) wavelet with a relative low degree is chosen to construct a sparse orthogonal wavelet matrix.