  In this paper we are concerned with Trefftz discretizations of the
time-dependent linear wave equation in anisotropic media in arbitrary space
dimensional domains $\Omega \subset \mathbb{R}^d~ (d\in \mathbb{N})$. We
propose two variants of the Trefftz DG method, define novel plane wave basis
functions based on rigorous choices of scaling transformations and coordinate
transformations, and prove that the corresponding approximate solutions possess
optimal-order error estimates with respect to the meshwidth $h$ and the
condition number of the coefficient matrices, respectively. Besides, we propose
the global Trefftz DG method combined with local DG methods to solve the
time-dependent linear nonhomogeneous wave equation in anisotropic media. In
particular, the error analysis holds for the (nonhomogeneous) Dirichlet,
Neumann, and mixed boundary conditions from the original PDEs. Furthermore, a
strategy to discretize the model in heterogeneous media is proposed. The
numerical results verify the validity of the theoretical results, and show that
the resulting approximate solutions possess high accuracy.
