  In this paper we are concerned with plane wave discontinuous Galerkin (PWDG)
methods for Helmholtz equation and time-harmonic Maxwell equations in
three-dimensional anisotropic media, for which the coefficients of the
equations are matrices instead of numbers. We first define novel plane wave
basis functions based on rigorous choices of scaling transformations and
coordinate transformations. Then we derive the error estimates of the resulting
approximate solutions with respect to the condition number of the coefficient
matrices, under a new assumption on the shape regularity of polyhedral meshes.
Numerical results verify the validity of the theoretical results, and indicate
that the approximate solutions generated by the proposed PWDG method possess
high accuracy.
