The higher-order hierarchical Legendre basis functions combining the electrical field integral equations (EFIE) are developed to\nsolve the scattering problems from the rough surface.The hierarchical two-level spectral preconditioning method is developed for\nthe generalized minimal residual iterative method (GMRES). The hierarchical two-level spectral preconditioner is constructed by\ncombining the spectral preconditioner and sparse approximate inverse (SAI) preconditioner to speed up the convergence rate of\niterative methods.Themultilevel fastmultipole method (MLFMM) is employed to reduce memory requirement and computational\ncomplexity of the method of moments (MoM) solution. The accuracy and efficiency are confirmed with a couple of numerical\nexamples.
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