Abstract: Using the idea of the discontinuous Galerkin algorithm, we calculated a class of quasi-periodic scattering problem with a mixture of media and obstacles. The fundamental solution functions and Rayleigh-Bloch expansion were used to approximate behavior of the scattering field in the bounded regions and unbounded regions， respectively. The effectiveness of the algorithm was verified by numerical example.

Key words: discontinuous Galerkin algorithm, quasi-periodic scattering, Rayleigh-Bloch expansion, fundamental solution