Joint application of the incomplete Galerkin method and scattering matrix method for modeling multilayer diffraction gratings

A mathematical model of wave diffraction from a one-dimensional multilayer periodic grating is considered. A rigorous mathematical statement is given for the problem where partial radiation conditions are used for domain confinement. A complete formulation of the numerical algorithm based on a combination of the incomplete Galerkin method and the scattering-matrix method is presented. The algorithm’s convergence rate and computational complexity are analyzed and the optimal values of the computational parameters are recommended.