Regularized conjugate gradient method with fast multipole acceleration for wave scattering from 1D fractal rough surface

► An efficient and accurate regularized conjugate gradient method (RCGM) is proposed. ► The RCGM is designed to deal with the large scale scattering problem with tapered wave incidence. ► The selection of regularization parameter and the law of energy conservation are studied. ► The RCGM has the stronger stationary, the lower complexity, and it can improve calculation speed. ► The relationships between the parameters of rough surfaces and the scattered field are studied.