Wavelet Nyström fast numerical algorithm for the integral equation in scattering problems

Abstract

We present a fast Nyström algorithm to solving the inhomogeneous Lippmann– Schwinger equation for scattering wave field problems. This algorithm transforms the discrete matrix of the linear integral operator into a sparse matrix utilizing the compression property of the wavelet transform. The sparse linear equations are solved by the double conjugate gradient method. In the numerical part, we verified the feasibility and effectiveness of our method by modeling the wave field for a synthetic model.