Coifman wavelets in 3-D scattering from very rough random surfaces

The Coifman wavelets are employed to perform Galerkin's procedure in the method of moments (MoM). The Coiflets are continuous, smooth, overlapping, yet orthogonal, which permit significant reduction of the sampling rate and dramatic compression of the matrix size with respect to the pulse based MoM. In addition, the wavelet based impedance matrix is sparse. More importantly, the vanishing moments of the Coiflets of order L = 4 provide us with high precision O(h⁵) one-point quadrature, which knocks down the computational effort in filling the matrix entries from O(n²) to O(n). Our approach is different from the conventional wavelet technique, which employs wavelets to sparsify an existing impedance matrix under similarity transformation with computational cost in O(n²). Excellent agreement between this Coifman wavelet method and the previous publications is observed.