An approach of exact controllability combined with non-overlapping domain decomposition associated to the physical layer structure of air and coated material media is presented for simulations of the scattering of planar waves in 2-D coated aerodynamic shapes.Domain decomposition with non-matching finite element meshes at the interface is introduced,which allows to use different numbers of grid points required by different media.The conditions of compatibility at the interfaces between each subdomain are satisfied weakly by a Lagrange multiplier technique.The whole structure of the algorithm includes one outer loop for capturing time periodic solutions based on exact controllability and one inner loop for domain decomposed solutions through a treatment of Lagrange multiplier.Numerical results of the scattered fields are presented and compared for both perfectly conducting and coated aerodynamic shapes like 2-D airfoils,which reveal the effect of the coated layer.