A combined scheme of the local spectral element method and the generalized plane wave discontinuous Galerkin method for the anisotropic Helmholtz equation.

In this paper we first consider a special class of nonhomogeneous and anisotropic Helmholtz equation with variable coefficients and the source term. Combined with local spectral element method, a generalized plane wave discontinuous Galerkin method for the discretization of such Helmholtz equation is designed. Then we define new generalized plane wave basis functions for two-dimensional anisotropic Helmholtz equation with the variable coefficient. Besides, the error estimates of the approximation solutions generated by the proposed discretization method are derived. Especially, the orders of the condition number ρ of the anisotropic matrix in the error estimates are optimal. Finally, numerical results verify the validity of the theoretical results, and indicate that the new method possesses high accuracy and is slightly affected by the pollution effect for the large wavenumbers. [ABSTRACT FROM AUTHOR]